Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Concepts, Methods, and Paradigms Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

10. The Nonlinear Theory of Arch-Supported Structures

verfasst von : Walter Lacarbonara

Erschienen in: Nonlinear Structural Mechanics

Verlag: Springer US

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This chapter presents the nonlinear theory of arch-supported structures that exploit the large load-bearing capacities of arches when they are subject to compressional states of stress. These structures exhibit nonsymmetric precritical behaviors opposite to those of suspension cables (softening for downward loads and hardening for upward loads). The theory is shown in the context of a recent arch bridge design, the bridge called Ponte della Musica on the Tiber river in Rome. The elastic loss of stability due to both traffic-induced vertical loads and the flutter condition are investigated using flutter derivatives obtained in wind tunnel tests. The sensitivity of flutter with respect to important parameters such as the wind angle of attack, the level of prestress in the bridge, and structural damping is also elucidated.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel The Nonlinear Theory of Cable-Supported Structures
Nächstes Kapitel Discretization Methods
Literatur
1.
Abdel-Ghaffar AM (1980) Vertical vibration analysis of suspension bridges. ASCE J Struct Div 106:2053–2075
2.
Abdel-Ghaffar AM (1982) Suspension bridge vibration: continuum formulation. J Eng Mech-ASCE 108:1215–1232
3.
Abdel-Ghaffar AM, Rubin LI (1983) Nonlinear free vibrations of suspension bridges: theory. J Eng Mech-ASCE 109:313–345
4.
Abdel-Ghaffar AM, Khalifa MA (1991) Importance of cable vibrations in dynamics of cable-stayed bridges. J Eng Mech-ASCE 117:2571–2589
5.
Addessi D, Lacarbonara W, Paolone A (2005) On the linear normal modes of planar prestressed elastica arches. J Sound Vib 284:1075–1097
6.
Addessi D, Lacarbonara W, Paolone A (2005) Free in-plane vibrations of highly pre-stressed curved beams. Acta Mech 180:133–156
7.
Addessi D, Lacarbonara W, Paolone A (2005) Linear vibrations of planar pre-stressed arches undergoing static bifurcations. In: Proceedings of the EURODYN 2005, Paris, Sept 4–7, 2005
8.
Agar TJA (1989) The analysis of aerodynamic flutter of suspension bridges. Comput Struct 30:593–600
9.
Agar TJA (1989) Aerodynamic flutter analysis of suspension bridges by a modal technique. Eng Struct 11:75–82
10.
Akhtar I, Marzouk OA, Nayfeh AH (2009) A van der Pol-Duffing oscillator model of hydrodynamic forces on canonical structures. J Comput Nonlin Dyn 4:041006-1-9
11.
Akhtar I, Nayfeh AH, Ribbens CJ (2009) On the stability and extension of reduced-order Galerkin models in incompressible flows: a numerical study of vortex shedding. Theor Comp Fluid Dyn 23:213–237
12.
Allan W (1874) Theory of arches. D. Van Nostrand, New York
13.
Allgower EL, Georg K (1990) Numerical continuation methods: an introduction. Springer, Berlin
14.
Allgower EL, Georg K (1997) Numerical path following. In: Ciarlet PG, Lions JL (eds) Handbook of numerical analysis, vol 5. North-Holland, Delft, NL, pp 3–207
15.
Ames WF (1002) Numerical methods for partial differential equations, 3rd edn. Academic, New York
16.
Anderson TJ, Nayfeh AH, Balachandran B (1996) Experimental verification of the importance of the nonlinear curvature in the response of a cantilever beam. J Vib Acoust 118:21–27
17.
Andrade LG, Awruch AM, Morsch IB (2007) Geometrically nonlinear analysis of laminate composite plates and shells using the eight-node hexahedral element with one-point integration. Compos Struct 79(4):571–580
18.
Anselone PM, Moore RH (1966) An extension of the Newton Kantorovic method for solving nonlinear equations with an application to elasticity. J Math Anal Appl13:475–501
19.
Antman SS, Warner WH (1967) Dynamical theory of hyperelastic rods. Arch Rat Mech Anal 23:135–162MathSciNet
20.
Antman SS (1972) The theory of rods. In: Flügge S, Truesdell C (ed) Handbuch der Physik Via/2, pp 641–703
21.
Antman SS (1990) Global properties of buckled states of plates that can suffer thickness changes. Arch Ration Mech Anal 110:103–117MathSciNet
22.
23.
Antman SS (2005) Problems of nonlinear elasticity. Springer, New York
24.
Antman SS, Lacarbonara W (2009) Forced radial motions of nonlinearly viscoelastic shells. J Elast 96:155–190MathSciNet
25.
Arbabei F, Li F (1991) Buckling of variable cross-section columns. Integral–equation approach. J Struct Engng 117:2426–2441
26.
Arena A (2008) Modellazione non lineare ed analisi della risposta dinamica di ponti sospesi. MS Thesis (in Italian). Sapienza University of Rome
27.
Arena A, Formica G, Lacarbonara W, Dankowicz H (2011) Nonlinear finite element-based path following of periodic solutions. Paper no. DETC2011-48681, 2011 ASME IDETC, Washington DC USA, August 28–31, 2011
28.
Arvin H (2012) Nonlinear modal analysis of a rotating composite Timoshenko beam with internal resonance. PhD Dissertation, Amirkabir University (Iran) and Sapienza University of Rome (Italy)
29.
Arena A, Lacarbonara W, Marzocca P (2011) Nonlinear aeroelastic formulation for flexible high-aspect ratio wings via geometrically exact approach. Paper No. AIAA-11-937605, 52nd AIAA/ASME/ASCE/AHS Structures, Structural Dynamics & Materials Conference, Denver, CO, April 4–7, 2011
30.
Arena A, Lacarbonara W, Marzocca P (2011) Nonlinear dynamic stall flutter for flexible high-aspect ratio wings. ENOC 2011 7th European Nonlinear Dynamics Conference, Rome, July 24–29, 2011
31.
Arena A, Lacarbonara W, Marzocca P (2012) Nonlinear post-flutter analysis for flexible high-aspect-ratio wings. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, USA, April 23–27
32.
Arena A, Lacarbonara W (2012) Nonlinear parametric modeling of suspension bridges under aeroelastic forces. Nonlinear Dynam, DOI: 10.1007/s11071-012-0636-3
33.
Arena A, Lacarbonara W, Marzocca P (2012) Unsteady aerodynamic modeling and flutter analysis of long-span suspension bridges. Paper No. DETC2012/CIE-70289, ASME IDETC/CIE 2012, August 12–15, 2012, Chicago, IL
34.
Argyris J (1982) An excursion into large rotations. Comput Meth Appl Mech Eng 32:85–155MathSciNet
35.
Asplund SO (1943) On the deflection theory of suspension bridges. Alqvist & Wiksells boktryckeri. Uppsala, Stockholm
36.
Atluri S (1973) Nonlinear vibrations of a hinged beam including nonlinear inertia effects. J Appl Mech 40:121–126
37.
Augusti G, Spinelli P, Borri C, Bartoli G, Giachi M, Giordano S (1995) The CRIACIV Atmospheric Boundary Layer Wind Tunnel. In: Wind engineering: retrospect and prospect, IAWE, International Association for Wind Engineering, vol. 5, Wiley Eastern Limited, New Delhi
38.
Auricchio F, Taylor RL (1997) Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior. Comput Method Appl M 143:175–194
39.
Auricchio F, Taylor RL, Lubliner J (1997) Shape-memory alloys: macro-modelling and numerical simulations of the superelastic behavior. Comput Method Appl M 146:281–312
40.
Auricchio F, Petrini L (2004) A three-dimensional model describing stress-temperature induced solid phase transformations. Part I: solution algorithm and boundary value problems. Int J Numer Methods Eng 61:807–836
41.
Auricchio F, Petrini L (2004) A three-dimensional model describing stress-temperature induced solid phase transformations. Part II: thermomechanical coupling and hybrid composite applications. Int J Numer Methods Eng 61:716–737
42.
Avramov KV, Pierre C, Shyriaieva NV (2008) Nonlinear equations of flexural-flexural-torsional oscillations of rotating beams with arbitrary cross-section. Int Appl Mech 44: 582–589MathSciNet
43.
Ball JM (1978) Finite-time blow-up in nonlinear problems. Nonlinear Evolution Equations. Academic, New York, pp 189–205
44.
Balachandran B, Preidikman S (2004) Oscillations of piezoelectric micro-scale resonators. In: Topping BHV, Mota Soares CA (eds) Computational structures technology, progress in computational structures technology, pp 327–352
45.
Ban RE, Chan TF (1986) PLTMGC: A multi-grid continuation program for parameterized nonlinear elliptic systems. SIAM J Sci Stat Comput 7:540–559
46.
Bank RE (1998) PLTMG: A software package for solving elliptic partial differential equations, Users’ Guide 8.0. Software, Environments and Tools 5. J Soc Ind Appl Math
47.
Bardin BS, Markeyev AP (1995) The stability of the equilibrium of a pendulum for vertical oscillations of the point of suspension. J Appl Math Mech 59:879–886MathSciNet
48.
Bartoli G, Righi M (2006) Flutter mechanism for rectangular prisms in smooth and turbulent flow. J Wind Eng Ind Aerodyn 94:275–291
49.
Başar Y, Krätzig WB (1985) Mechanik der Flächentragwerke. Friedrich Vieweg & Sohn, Braunschweig/Wiesbaden
50.
Başar Y (1987) A consistent theory of geometrically non-linear shells with an independent rotation vector. Int J Solids Struct 23:1401–1415
51.
Başar Y (1993) Finite-rotation theories for arbitrary composite laminates. Acta Mech 98:159–176MathSciNet
52.
Başar Y, Montag U, Ding Y (1993) On a isoparametric finite-element for composite laminates with finite rotation. Comput Mech 12:329–348
53.
Başar Y, Ding Y, Schultz R (1993) Refined shear-deformation models for composite laminates with finite rotations. Int J Solids Struct 30:2611–2638
54.
Başar Y, Itskov M, Eckstein A (2000) Composite laminates: nonlinear interlaminar stress analysis by multi-layer shell elements. Comput Method Appl Mech Engrg 185:367–397
55.
Batra RC (2006) Elements of continuum mechanics. AIAA Educational Series
56.
Batra RC (2007) Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates. Thin-Walled Struct 45:974–982
57.
Batra RC, Porfiri M, Spinello D (2006) Electromechanical model of electrically actuated narrow microbeams. J Microelectromech S 15:1175–1189
58.
Batra RC, Porfiri M, Spinello D (2008) Vibrations of narrow microbeams predeformed by an electric field. J Sound Vib 309:600–612
59.
Bazant Z, Cedolin L (1991) Stability of structures. Oxford University Press, New York
60.
Behal A, Marzocca P, Rao VM, Gnann A (2006) Nonlinear adaptive control of an aeroelastic two-dimensional lifting surface. J Guid Contr Dynam 29:382–390
61.
Beletsky VV, Levin EM (1993) Dynamics of space tether systems. Advances in the astronautical sciences, vol 83. American Astronautical Society, San Diego
62.
Belyayev NM (1924) Stability of prismatic rods subject to variable longitudinal forces (in Russian), in Engineering construction and structural mechanics, Leningrad
63.
Benedetti D, Brebbia C, Cedolin, L (1972) Geometrical nonlinear analysis of structures by finite elements. Meccanica 7:1–10
64.
Bernardini D, Pence TJ (2002) Shape-memory materials, modeling. In: Schwartz M (ed) The encyclopedia of smart materials, vol 2. Wiley, New York, pp 964–980
65.
Bernardini D, Pence TJ (2009) Mathematical models for shape memory materials. In: Schwartz M (ed) Smart materials. CRC Press, Boca Raton, pp 20.17–20.28
66.
Beran PS, Strganac, TW, Kim K, Nichkawde C (2004) Studies of store-induced Limit-Cycle Oscillations using a model with full system nonlinearities. Nonlinear Dynam 37:323–339
67.
Biezeno CB, Koch, J (1923) Over een nieuwe methode ter berekening van vlokke platen met toepassing op enkele voor de techniek belangrijke belastingsgevallen. Ing Grav 38:25–36
68.
Bigoni D (2012) Nonlinear solid mechanics. Bifurcation theory and material instability. Cambridge University Press, Cambridge.
69.
Bleich F, McCullough CB, Rosecrans R, Vincent GS (1950) The mathematical theory of vibration in suspension bridges: A Contribution to the work of the Advisoy Board on the Investigation of Suspension Bridges. Department of Commerce, Bureau of Public Roads, USGPO, Washington, DC
70.
Blekhman II (2000) Vibrational mechanics. Nonlinear dynamic effects, general approach, applications. World Scientific, Singapore
71.
Blevins RD (1977) Flow-induced vibration. Van Nostrand Reinhold, New York
72.
Boley BA, Weiner JH (1960) Theory of thermal stresses. Wiley, New York
73.
Bolotin VV (1964) The dynamic stability of elastic systems. Holden-Day, San Francisco
74.
Boonyapinyo V, Lauhatanon Y, Lukkunaprasit P (2006) Nonlinear aerostatic stability analysis of suspension bridges. Eng Struct28:793–803
75.
Borri M, Mantegazza P (1985) Some contributions on structural and dynamic modeling of helicopter rotor blades. L’Aerotecnica Missili e Spazio 64(9):143–154
76.
Bouc R (1967) Forced vibrations of mechanical systems with hysteresis. In: Preceedings of the 4th International Conference on Nonlinear Oscillations, Prague, Czechoslovakia
77.
Bouc R (1971) Modele mathematique dhysteresis. Acustica 24:16–25
78.
Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer, Berlin
79.
Brokate M, Sprekels J (1996) Hysteresis and phase transitions. Springer, New York
80.
Brownjohn JMW (1994) Observations on non-linear dynamic characteristics of suspension bridges. Earthquake Eng Struc 23:1351–1367
81.
Brownjohn JMW, Dumanoglu AA, Taylor CA (1994) Vibration characteristics of a suspension footbridge. Eng Struct 16:395–406
82.
Brownjohn JMW (1996) Vibration characteristics of a suspension footbridge. J Sound Vib 202:29–46
83.
Buechner HF, Johnson MW, Moore RH (1965) The calculation of equilibrium states of elastic bodies by Newton’s method. Proceedings of the 9th Mid Western Mech Conf, Madison
84.
Burgess JJ, Triantafyllou MS (1988) The elastic frequencies of cables. J Sound Vib 120: 153–165
85.
Burgess JJ (1993) Bending stiffness in a simulation of undersea cable deployment. Int J Offshore Polar Eng 3:197–204
86.
Caflisch R, Maddocks JH (1984) Nonlinear dynamical theory of the elastica. Proc R Soc Edin 99A:1–23MathSciNet
87.
Capecchi D, Vestroni F (1985) Steady-state dynamic analysis of hysteretic systems. J Eng Mech-ASCE 111:1515–1531
88.
Capecchi D, Vestroni F (1990) Periodic response of a class of hysteretic oscillators. Int J Non Linear Mech 25:309–317
89.
Carpineto N, Vestroni F, Lacarbonara W (2011) Vibration mitigation by means of hysteretic tuned mass dampers. In: Proceedings of EURODYN 2011, Leuven, July 4–5, 2011
90.
Carpineto N (2011) Hysteretic tuned mass dampers for structural vibration mitigation. PhD Dissertation, Sapienza University of Rome
91.
Carrera E (1999) Transverse normal stress effects in multilayered plates. J Appl Mech 66: 1004–1012
92.
Carrera E, Parisch H (1997) An evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells. Compos Struct 40(1):11–24
93.
Carrera E (2002) Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Method E 9:87–140MathSciNet
94.
Carrera E, Ciuffreda A (2005) A unified formulation to assess theories of multi-layered plates for various bending problems. Compos Struct 69:271–93
95.
Cartmell M (1990) Introduction to linear, parametric and nonlinear vibrations. Chapman and Hall, London
96.
Casciaro R (2005) Computational asymptotic post–buckling analysis of slender elastic structures, CISM Courses and Lectures NO. 470. Springer, New York
97.
Castro FM (1991) Mechanical switches snap back. Mach Des 63:56–61
98.
Caughey TK (1960) Sinusoidal excitation of a system with bilinear hysteresis. J Appl Mech 643:640–643MathSciNet
99.
Cesari L (1971) Asymptotic behavior and stability problems in ordinary differential equations. Springer, Berlin
100.
Cevik M, Pakdemirli M (2005) Non-linear vibrations of suspension bridges with external excitation. Int J Non Linear Mech 40:901–923
101.
Chan TF, Keller HB (1982) Arc-length continuation and multi-grid techniques for nonlinear eigenvalue problems. SIAM J Sci Statist Comput 3:173–194MathSciNet
102.
Chang WK, Pilipchuk V, Ibrahim RA (1997) Fluid flow-induced nonlinear vibration of suspended cables. Nonlinear Dynam 14:377–406MathSciNet
103.
Chelomeĭ V N (1939) The dynamic stability of elements of aircraft structures. Aeroflot, Moscow
104.
Chen X, Matsumoto M, Kareem A (2000) Time domain flutter and buffeting response analysis of bridges. J Eng Mech-ASCE 126:7–16
105.
Chen X, Kareem A (2000) Advances in modeling of aerodynamic forces on bridge decks. J Eng Mech 128:1193–1205
106.
Cheng J, Jiang J-J, Xiao R-C, Xiang H-F (2003) Series method for analyzing 3D nonlinear torsional divergence of suspension bridges. Comput Struct 81:299–308
107.
Cheng J, Jiang J-J, Xiao R-C (2003) Aerostatic stability analysis of suspension bridges under parametric uncertainty. Eng Struct 25:1675–1684
108.
Cheng SH, Lau DT, Cheung MS (2003) Comparison of numerical techniques for 3D flutter analysis of cable-stayed bridges. Comput Struct 81:2811–2822
109.
Chetayev NG (1961) The stability of motion. Pergamon Press, New York
110.
Cheung YK (1968) The finite strip method in the analysis of elastic plates with two opposite simply supported ends. Proc Instn Civ Engrg Lond 40:1–7
111.
Cho KN, Bert CW, Striz AG (1991) Free vibrations of laminated rectangular plates analyzed by higher order individual-layer theory. J Sound Vib 145(3):429–442
112.
Cho MH, Parmerter RR (1993) Efficient higher-order composite plate-theory for general lamination configurations. AIAA J 31(7):1299–1306
113.
Ciarlet PG, Destuynder PA (1979) Justification of a nonlinear model in plate theory. Comp Method Appl Mech Engrg 17/18:227–258
114.
Ciarlet PG (2002) The finite element method for elliptic problems. Society for Industrial and Applied Mathematics, Philadelphia, PA
115.
Clark R, Cox D, Curtiss HCJ, Edwards JW, Hall KC, Peters DA, Scanlan RH, Simiu E, Sisto F, Strganac Th W (2004) A modern course in Aeroelasticity. Series: Solid mechanics and its applications 116, 4th edn. Kluwer Academic, New York
116.
Coddington EA, Levinson N (1955) Theory of ordinary differential equations. McGraw-Hill Book, New York
117.
COMSOL Multiphysics (2008) COMSOL Multiphysics/User’s Guide Version 3.5. COMSOL AB, Stokholm, Sweden
118.
Connor J, Morin R (1970) Perturbation techniques in the analysis of geometrically nonlinear shells. In: Proc Symp Int Union of Theoretical and Applied Mechanics, Liege, vol 61, 683–705
119.
Cosmo ML, Lorenzini EC (1997) Tethers in space handbook, 3rd edn. Smithsonian Astrophisical observatory. NASA Marshall Space Flight Center, Huntsville, Alabama
120.
Costello GA (1997) Theory of wire rope. Springer, New York
121.
Cosserat EF (1909) Theorie de corps deformables. Hermann, Paris
122.
Crandall SH (1956) Engineering analysis. McGraw-Hill, New York
123.
Crespo da Silva MRM, Hodges DH (1986) Nonlinear flexure and torsion of rotating beams with application to helicopter rotor blades-I. Formulation. Vertica 10:151–169
124.
Crespo da Silva MRM, Glynn CVC (1978) Nonlinear flexural-flexural-torsional dynamics of inextensional beams I. Equations of motion. J Struct Mech 6:437–448
125.
Crespo da Silva MRM (1988) Nonlinear flexural-flexural-torsional-extensional dynamics of beams-II. Response analysis. Int J Solids Struct 24:1235–1242
126.
Crisfield MA (1991) Non-Linear Finite Element Analysis of Solids and Structures, vol 1. Wiley, New York
127.
Crisfield MA (1997) Non-linear finite element analysis of solids and structures, vol. 2. Wiley, New York
128.
Dankowicz H, Schilder F (2011) An extended continuation problem for bifurcation analysis in the presence of constraints. J Comput Nonlinear Dyn 6:031003
129.
Davenport AG (1966) The action of wind on suspension bridges. In: Int Symp on Suspension Bridges, Lisbon, 79–100
130.
Demasi L (2009) ∞ 6 Mixed plate theories based on the Generalized Unified Formulation. Part I: Governing equations. Compos Struct 87:1–11. Part V: Results. Compos Struct 88:1–16
131.
De Miranda M (1998) Storebaelt East Bridge - Aspetti del montaggio e della realizzazione (in Italian). Costruzioni Metalliche 6
132.
Den Hartog JP (1934) Mechanical vibrations. McGraw-Hill, New York
133.
Depuis GA, Pfaffinger DD, Marcal PV (1970) Effective use of the incremental stiffness matrices in nonlinear geometric analysis. In: Proc Symp Int Union of Theoretical and Applied Mechanics, Liège, vol 61, 707–725
134.
Diana, G, Bruni S, Collina A, Zasso A (1998) Aerodynamic challenges in super long span bridge design. In: Larsen A, Esdahl E (eds) Proceedings of the International Symposium on Advances in Bridge Aerodynamics, 10–13 May, Copenhagen. Balkema, Rotterdam
135.
Ding Q, Chen A, Xiang H (2002) Coupled flutter analysis of long-span bridges by multimode and full-order approaches. J Wind Eng Ind Aerodyn 90:1981–1993
136.
Dinnik AN (1929) Design of columns of varying cross section. Trans ASME 51:105–114
137.
Dinnik AN (1932) Design of columns of varying cross section. Trans ASME 54:165–171
138.
Di Egidio A, Luongo A, Paolone A (2007) Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams. Int J Non Linear Mech 42:88–98
139.
Di Sciuva M, Icardi U (1995) Analysis of thick multilayered anisotropic plates by a higher-order plate element. AIAA J 33(12):2435–2437
140.
Doedel EJ, Paffenroth RC, Champneys AR, Fairgrieve TF, Kuznetsov, Yu A, Sandstede B, Wang X (2001) AUTO 2000: Continuation and bifurcation software for ordinary differential equations (with HomCont), Technical Report, Caltech
141.
Drozdov AD (1996) Finite elasticity and viscoelasticity. World Scientific, Singapore
142.
Ecker H, Dohnal F, Springer H (2005) Enhanced damping of a beam structure by parametric excitation. In: Proceedings of European Nonlinear Oscillations Conf. (ENOC-2005) Eindhoven, NL
143.
El-Bassiouny AF (2007) Parametric excitation of internally resonant double pendulum. Phys Scripta 76:173–186
144.
Einaudi R (1936) Sulle configurazioni di equilibrio instabile di una piastra sollecitata da sforzi tangenziali pulsanti. Atti Accad Gioenia Catania 1 (serie 6), mem. XX:1–20
145.
Eisley JG (1964) Nonlinear vibration of beams and rectangular plates. Z Angew Math Mech 15:167–175MathSciNet
146.
Elishakoff I (2000) Both static deflection and vibration mode of uniform beam can serve as a buckling mode of a non-uniform column. J Sound Vib 232:477–489MathSciNet
147.
Elishakoff I (2005) Eigenvalues of inhomogeneous structures. CRC Press, Boca Raton
148.
Engesser F (1909) Ueber die Knickfestigkeit von Staeben veraenderlichen Traegheitsmomentes (in German). Zeitschrift der Oesterreichischer Ingenieur und Architekten Verein 34:506–508
149.
Eringen AC (1976) Nonlocal field theories. In: Eringen AC (ed) Continuum physics, vol 4. Academic, New York
150.
Euler L (1759) Sur la force des colonnes (in French). Memoires de L’Academie des Sciences et Belles-Lettres 13:252–282
151.
Evensen JA, Evan-Iwanowski RM (1996) Effects of longitudinal inertia upon the parametric response of elastic columns. J Appl Mech 33:141–148
152.
Faedo S (1949) Un nuovo metodo per l’analisi esistenziale e quantitativa dei problemi di propagazione. Ann Sc Norm Sup Pisa - Classe di Scienze, Ser. 3,1 no. 1–4:1–41
153.
Faraday M (1831) On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces. Philos Tr R Soc S-A 121:299
154.
Farquharson FB, Smith, FC, Vincent GS (1950) Aerodynamic stability of suspension bridges with special reference to the Tacoma Narrows Bridge. Part II: Mathematical analyses. Bulletin 116. University of Washington Press, Engineering Experimental Station, Seattle, WA
155.
Ferreira AJM, Roque CMC, Martins PALS (2004) Radial basis functions and higher-order shear deformation theories in the analysis of laminated composite beams and plates. Compos Struct 66:287–293
156.
Fiedler L, Lacarbonara W, Vestroni F (2007) Vibration behavior of thick composite laminated plates subject to in-plane pre-stress loading. In: Proceedings of the DECT’07–2007 ASME Engineering Technical Conferences, DECT2007–35532, Las Vegas, Nevada, 4–7 September 2007
157.
Fiedler L, Lacarbonara W, Vestroni F (2009) A general higher-order theory for multi-layered, shear-deformable composite plates. Acta Mech209:85–98
158.
Fiedler L., Lacarbonara W., Vestroni F (2010) A generalized higher-order theory for buckling of thick multi-layered composite plates with normal and transverse shear strains. Compos Struct 92:3011–3020
159.
Finlayson BA (1972) The method of weighted residuals and variational principles. Academic, New York
160.
161.
Fonda A, Schneider Z, Zanolin F (1994) Periodic oscillations for a nonlinear suspension bridge model. J Comput Appl Math 52:113–140MathSciNet
162.
Föppl A (1907) Vorlesungen über technische Mechanik, B.G. Teubner, Bd. 5., Leipzig
163.
Formica G, Lacarbonara W, Alessi R (2010) Vibrations of carbon nanotube-reinforced composites. J Sound Vib 329:1875–1889
164.
Formica G, Arena A, Lacarbonara W, Dankowicz H (2013) Coupling FEM with parameter continuation for analysis and bifurcations of periodic responses in nonlinear structures. J Comput Nonlin Dyn 8, 021013
165.
Frahm H (1911) Device for damping vibration of bodies, US Patent 989958
166.
Fremond M (2002) Non-smooth thermomechanics. Springer, Berlin
167.
Frisch-Fay R (1962) Flexible bars. Butterworths, Washington, D.C
168.
Fung YC (1990) Biomechanics: motion, flow, stress, and growth. Springer, New York
169.
Garcea G, Trunfio GA, Casciaro R (2002) Path-following analysis of thin-walled structures and comparison with asymptotic post-critical solutions. Int J Numer Methods Eng 55:73–100
170.
Galerkin BG (1915) Series occurring in some problems of elastic stability of rods and plates. Eng Bull 19:897–908
171.
Ganapathi M, Makhecha DP (2001) Free vibration analysis of multi-layered composite laminates based on an accurate higher-order theory. Compos Part B-Eng 32:535–543
172.
Gattulli V, Lepidi M (2003) Nonlinear interactions in the planar dynamics of cable-stayed beam. Int J Solids Struct 40:4729–4748
173.
Gattulli V, Lepidi M, Macdonald JHG, Taylor CA (2005) One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models, Int J Non-Linear Mech 40:571–588
174.
Gaudenzi P (1992) A general formulation of higher-order theories for the analysis of composite laminated plates. Compos Struct 20:103–112
175.
Gaudenzi P, Barboni R, Mannini A (1995) A finite element evaluation of single-layer and multi-layer theories for the analysis of laminated plates. Compos Struct 30:427–440
176.
Ge Z, Kruse HP, Marsden JE (1996) The limits of Hamiltonian structures in three dimensional elasticity, shells, and rods. J Nonlinear Sci 6:19–57MathSciNet
177.
Gimsing NJ (1997) Cable supported bridges: concept and design, 2nd edn. Wiley, New York
178.
Lanzara G, Yoon Y, Liu H, Peng S, Lee W-I (2009) Carbon nanotube reservoirs for self-healing materials. Nanotechnology 20:335704
179.
Glauert H (1947) The elements of Aerofoil and Airscrew theory, 2nd edn. Cambridge University Press, New York
180.
Glover J, Lazer AC, McKenna PJ (1989) Existence and stability of large scale nonlinear oscillations in suspension bridges. ZAMP 40:172–200MathSciNet
181.
Goldstein H, Poole CP, Safko JL (2002) Classical mechanics, 3rd edn. Addison Wesley, Reading
182.
Guckenheimer J, Holmes P (1985) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, New York
183.
Hafka RT, Mallet RH, Nachbar W (1971) Adaptation of Koiter’s method to finite element analysis of snap-through buckling behaviour. Int J Solids Struct 7:1427–1447
184.
Hale JK (1969) Ordinary differential equations. Wiley-Interscience, New York
185.
Hall BD, Preidikman S, Mook DT, Nayfeh AH (2001) Novel strategy for suppressing the flutter oscillations of aircraft wings. AIAA J 39:1843–1850
186.
Han S-C, Tabiei A, Park W-T (2008) Geometrically nonlinear analysis of laminated composite thin shells using a modified first-order shear deformable element-based Lagrangian shell element. Compos Struct 82(3):465–474
187.
Handbook (1986) Tethers in space. in Proceedings of the first International Conference on Tethers in Space, Sept 17–19, Arlington, VA
188.
Handbook (1988) Space Tethers for Science in the Space Station Era, Societá Italiana di Fisica, Conference Proceedings, 14, Bologna
189.
Hansen MH, Gaunaa M, Madsen HAA (2004) A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations, Report No. R -1354(EN), Risø National Laboratory
190.
Hartlen R, Currie I (1970) Lift-oscillator model for vortex-induced vibration. Proc Am Soc Civ Eng 96:577–591
191.
Hirai A, Okauchi I, Miyata T (1966) On the behaviour of suspension bridges under wind action. Paper No. 8. Int. Sypm. on Suspension Bridges, Lisbon, 240–256
192.
Hodges DH, Dowell EH (1974) Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. NASA TN D-7818
193.
Hodges DH, Atilgan AR, Danielson DA (1993) A geometrically nonlinear theory of elastic plates. J Appl Mech 60:109–1126
194.
Hodges DH, Atilgan AR, Danielson DA (1993) A geometrically nonlinear theory of elastic plates. J Appl Mech 60:109–116
195.
Hodges DH (1999) Non-linear in-plane deformation and buckling of rings and high arches. Int J Non Linear Mech 34:723–737
196.
Hodges DH, Wenbin Y, Mayuresh JP (2009) Geometrically-exact, intrinsic theory for dynamics of moving composite plates. Int J Solids Struct 46:2036–2042
197.
Holzapfel GA (2000) Nonlinear solid mechanics. Wiley, Chichester
198.
Hsu CS (1963) On the parametric excitation of a dynamic system with multiple degrees of freedom. J Appl Mech 30:367–372
199.
Hua XG, Chen ZQ (2008) Full-order and multimode flutter analysis using ANSYS. Finite Elem Anal Des 44:537–551
200.
Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. Prentice Hall, Upper Saddle River
201.
Ibrahim RA (2004) Nonlinear vibrations of suspended cables - Part III: Random excitation and interaction with fluid flow. Appl Mech Rev 57:515–549
202.
Ibrahim RA (2005) Liquid sloshing dynamics. Theory and applications. Cambridge University Press, Cambridge
203.
Ibrahim RA (2008) Parametric random vibration. New York, Dover
204.
Iooss G, Adelmeyer M (1992) Topics in bifurcation theory and applications. World Scientific, Singapore
205.
In-Soo S, Uchiyama Y, Yabuno H, Lacarbonara W (2008) Simply supported elastic beams under parametric excitation. Nonlinear Dynam 53:129–138MathSciNet
206.
Irvine HM, Caughey TK (1974) The linear theory of free vibrations of a suspended cable. Proc R Soc London, Ser A 341:299–315
207.
Irvine HM (1984) Cable structures. Dover Publications, New York
208.
Iwan WD (1965) The steady-state response of the double bilinear hysteretic oscillator. J Appl Mech 32:921–925MathSciNet
209.
Iwan WD, Blevins RD (1974) A model for vortex induced oscillation of structures. J Appl Mech Trans ASME 41:581–586
210.
Jacobs EN, Ward KE, Pinkerton RM (1933) The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel. NACA Report No. 460
211.
Jacover D, McKenna PJ (1994) Nonlinear torsional flexings in a periodically forced suspended beam. J Comput Appl Math 52:241–265MathSciNet
212.
Jensen JS (1998) Non-linear dynamics of the follower-loaded double pendulum with added support-excitation. J Sound Vib 215:125–142
213.
Jones RM (1975) Mechanics of composite materials. McGraw-Hill Book Company, New York
214.
Jones KF (1992) Coupled vertical and horizontal galloping. J Eng Mech-ASCE 118:92–106
215.
Johnson MW Jr, Urbanik TJ (1984) A nonlinear theory for elastic plates with application to characterizing paper properties. J Appl Mech 51:146–152
216.
Kantorovich LV, Krylov VI (1964) Approximate methods of higher analysis. Interscience Publishers, New York
217.
Kapitza PL (1965) Collected Papers of P.L. Kapitza, Edited by D. TerHarr, Pergamon Press, NY
218.
Krauskopf B, Osinga HM, Galan-Vioque J (eds) (2007) Numerical continuation methods for dynamical systems. Springer and Canopus Publishing Limited, New York
219.
Krylov N, Bogoliubov N (1935) Influence of resonance in transverse vibrations of rods caused by periodic normal forces at one end. Ukrainian Sc. Res. Inst. of Armament, Recueil Kiev.
220.
Kevorkian J, Cole JD (1996) Multiple scale and singular perturbation methods. Springer, New York
221.
Kienzler R, Bose DK (2008) Material conservation laws established within a consistent plate theory. In: Jaiani G, Podio-Guidugli P (eds) Proc symp int union of theoretical and applied mechanics on relations of shell plate beam and 3D models, Tbilisi, Georgia, April 23–27, 2007
222.
Ko JW, Strganac TW; Kurdila AJ (1998) Stability and control of a structurally nonlinear aeroelastic system. J Guid Control Dynam 21:718–725
223.
Komatsu S, Sakimoto T (1977) Ultimate load carrying capacity of steel arches. J Struct Div-ASCE 103(12):2323–2336
224.
Koiter WT (1945) On the stability of elastic equilibrium. PhD Thesis, Delft. English transl
225.
Koiter WT (1970) On the stability of elastic equilibrium (Translation from Dutch). Tech. Rep. AFFDL-TR-70-25, Airforce Flight Dynamics Lab
226.
Koiter WT (1970) Comment on: The linear and non-linear equilibrium equations for thin elastic shells according to the Kirchhoff–Love hypotheses. Int J Mech Sci 12:663–664
227.
Kholostova OV (2009) On the motions of a double pendulum with vibrating suspension point. Mech Sol 44:184–197
228.
Krupa M, Poth W, Schagerl M, Steindl A, Steiner W, Troger H, Wiedermann G (2006) Modelling, dynamics and control of tethered satellite systems. Nonlinear Dynam 43:73–96MathSciNet
229.
Kuhlmann G (2003) Ein hierarchisches inhomogenes Volumenelement zur Berechnung dickwandiger Faserverbunde. Ph.D. Thesis, Shaker Verlag, Aachen, Germany
230.
Yuri A. Kuznetsov YA (2004) Elements of applied bifurcation theory. Springer, New-York
231.
Hartman P (1982) Ordinary differential equations. Birkhaüser, Boston
232.
Iyengar NGR (1998) Structural stability of columns and plates. Wiley, New York
233.
Lacarbonara W, Chin CM, Nayfeh, AH (1997) Two-to-one internal resonances in parametrically excited buckled beams. AIAA Paper No. 97–1081, 38th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics & Materials Conf, Kissimmee, FL
234.
Lacarbonara W, Nayfeh AH, Kreider W (1998) Experimental validation of reduction methods for nonlinear vibrations of distributed-parameter systems: analysis of a buckled beam. Nonlinear Dynam 17:95–117
235.
Lacarbonara W (1999) Direct treatment and discretizations of non-linear spatially continuous systems. J Sound Vib 221:849–866MathSciNet
236.
Lacarbonara W, Vestroni F (2002) Feasibility of a vibration absorber based on hysteresis. In: Proceedings of Third World Congress on Structural Control, Como, April 7–12, 2002
237.
Lacarbonara W, Rega G, Nayfeh AH (2003) Resonant nonlinear normal modes. Part I: analytical treatment for structural one-dimensional systems. Int J Non Linear Mech 38:851–872
238.
Lacarbonara W, Rega G (2003) Resonant nonlinear normal modes. Part II: activation/orthogonality conditions for shallow structural systems. Int J Non Linear Mech 38: 873–887
239.
Lacarbonara W, Chin CM, Soper RR (2002) Open-loop nonlinear vibration control of shallow arches via perturbation approach. J Appl Mech 69:325–334MathSciNet
240.
Lacarbonara W, Vestroni F (2003) Nonclassical responses of oscillators with hysteresis. Nonlinear Dynam 32:235–258
241.
Lacarbonara W, Bernardini D, Vestroni, F (2004) Nonlinear thermomechanical oscillations of shape-memory devices. Int J Solids Struct 41:1209–1234
242.
Lacarbonara W, Paolone A, Yabuno, H (2004) Modeling of planar nonshallow prestressed beams towards asymptotic solutions. Mech Res Commun 31:301–310
243.
Lacarbonara W, Camillacci R (2004) Nonlinear normal modes of structural systems via asymptotic approach. Int J Solids Struct 41:5565–5594
244.
Lacarbonara W, Arafat HN, Nayfeh AH (2005) Nonlinear interactions in imperfect beams at veering. Int J Non Linear Mech 40:987–1003
245.
Lacarbonara W, Paolone A, Vestroni F (2005) Galloping instabilities in geometrically nonlinear cables under steady wind forces, Paper. No. 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, Sept 25–28
246.
Lacarbonara W, Yabuno H (2006) Refined models of elastic beams undergoing large in-plane motions: theory and experiment. Int J Solids Struct 43:5066–5084
247.
Lacarbonara W, Yabuno H, Hayashi K (2007) Nonlinear cancellation of the parametric resonance in elastic beams: theory and experiment. Int J Solids Struct 44:2209–2224
248.
Lacarbonara W, Antman SS (2007) Parametric resonances of nonlinearly viscoelastic rings subject to a pulsating pressure. 21st ASME DETC Conf, No. DETC2007-35245, Las Vegas, USA
249.
Lacarbonara W, Paolone A, Vestroni F (2007) Elastodynamics of nonshallow suspended cables: linear modal properties. J Vib Acoust 129:425–433
250.
Lacarbonara W, Paolone A, Vestroni F (2007) Nonlinear modal properties of nonshallow cables. Int J Non Linear Mech 42:542–554
251.
Lacarbonara W, Colone V (2007) Dynamic response of arch bridges traversed by high-speed trains. J Sound Vib 304:72–90
252.
Lacarbonara W, Paolone A (2007) Solution strategies to Saint–Venant problem. J Comput Appl Math 206:473–497MathSciNet
253.
Lacarbonara W (2008) Buckling and post-buckling of non-uniform non-linearly elastic rods. Int J Mech Sci 50:1316–1325
254.
Lacarbonara W, Pacitti A (2008) Nonlinear modeling of cables with flexural stiffness. Math Probl Eng, Article ID 370767, 21 pages, 2008. doi:10.1155/2008/370767
255.
Lacarbonara W, Antman, SS (2012) Parametric instabilities of the radial motions of nonlinearly viscoelastic shells subject to pulsating pressures. Int J Non Linear Mech  47:461–472
256.
Lacarbonara W, Ballerini S (2009) Vibration mitigation of a guyed mast via tuned pendulum dampers. Struct Eng Mech 32
257.
Lacarbonara W, Arena A (2011) Flutter of an arch bridge via a fully nonlinear continuum formulation. J Aerospace Eng 24:112–123
258.
Lacarbonara W, Pasquali M (2011) A geometrically exact formulation for thin multi-layered laminated composite plates. Compos Struct 93:1649–1663
259.
Lacarbonara W, Antman SS (2007) Parametric resonances of nonlinearly viscoelastic rings subject to a pulsating pressure. Paper DETC 2007–35245, 21th ASME Biennial Conf. on Mechanical Vibration and Noise
260.
Lacarbonara W, Antman SS (2008) What is parametric resonance in structural dynamics. Proceedings of the 6th Euromech Nonlinear Dynamics Conf., St. Petersburg, Russia
261.
Lacarbonara W, Arvin, H, Bakhtiari-Nejad, F (2012) A geometrically exact approach to the overall dynamics of elastic rotating blades – part 1: linear modal properties. Nonlinear Dynam, 70:659–675
262.
Lacarbonara W, Cetraro M (2011) Flutter control of a lifting surface via visco-hysteretic vibration absorbers. Int J Aeronautical Space Sci 12(4):331–345
263.
Lagoudas DC (ed) (2010) Shape memory alloys: modeling and engineering applications. Springer, New York
264.
Lanzo AD, Garcea G, Casciaro R (1995) Koiter post–buckling analysis of elastic plates. Int J Numer Methods Eng 38:2325–2345
265.
Lau DT, Cheung MS, Cheng SH (2000) 3D flutter analysis of bridges by spline finite-strip method. J Struct Eng-ASCE 126:1246–1254
266.
Lazer AC, McKenna PJ (1990) Large-amplitude periodic oscillations in suspension bridges: some new connection with nonlinear analysis. SIAM Rev 32:537–578MathSciNet
267.
Lee HK, Simunovic S (2001) A damage constitutive model of progressive debonding in aligned discontinuous fiber composites. Int J Solids Struct 38:875–895
268.
Lee CL, Perkins NC (1995) Three-dimensional oscillations of suspended cables involving simultaneous internal resonances. Nonlinear Dynam 8:45–63MathSciNet
269.
Lee J (1997) Thermally induced buckling of laminated composites by a layer-wise theory. Compos Struct 65:917–922
270.
Lee SY, Kuo YH (1991) Elastic stability of non-uniform columns. J Sound Vib 148:11–24
271.
Leipholz H (1970) Stability theory. Academic, New York
272.
Leissa AW (1969) Vibration of plates. NASA SP-160
273.
Li H, Balachandran B (2006) Buckling and free oscillations of composite microresonators. J Microelectromech Syst 15:42–51
274.
Li H, Balachandran B (2006) Buckling and free oscillations of composite microresonators. J Microelectromech S 15:42–51
275.
Li H, Preidikman S, Balachandran B, Mote Jr. CD (2006) Nonlinear free and forced oscillations of piezoelectric microresonators. J Micromech Microeng 16:356–367
276.
Li QS, Cao H, Li G (1994) Stability analysis of bars with multi-segments of varying cross-section. Comput Struct 53:1085–1089
277.
Li QS, Cao H, Li G (1995) Stability analysis of bars with varying cross-section. Int J Solids Struct 32:3217–3228
278.
Li QS, Cao H, Li G (1996) Static and dynamic analysis of straight bars with variable cross-section. Comput Struct 59:1185–1191
279.
Li QS (2000) Buckling analysis of multi-step non-uniform beams. Adv Struct Engng 3: 139–144
280.
Love AEH (1906) The mathematical theory of elasticity. Cambridge University Press, Cambridge
281.
Lubarda VA (2004) Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics. Appl Mech Rev 57:95–108
282.
Luongo A, Rega G, Vestroni F (1984) Planar non-linear free vibrations of an elastic cable. Int J Non Linear Mech 19:39–52
283.
Luongo A, Rega G, Vestroni F (1986) On nonlinear dynamics of planar shear undeformable beams. J Appl Mech 108:619–624
284.
Luongo A, Rega G, Vestroni F (1984) Planar non-linear free vibrations of an elastic cable. Int J Non Linear Mech 19:39–52
285.
Luongo A, Paolone A, Piccardo G (1998) Postcritical behavior of cables undergoing two simultaneous galloping modes. Meccanica 33:229–242
286.
Luongo A, Vestroni F (1994) Nonlinear free periodic oscillations of a tethered satellite system. J Sound Vib 175(3):299–315
287.
Luongo A (1997) Appunti di Meccanica delle Strutture. Lecture Notes (in Italian), L’Aquila
288.
Luongo A, Paolone A (2005) Scienza delle costruzioni, vol. 2: Il problema di de Saint Venant (in Italian). CEA, Milan
289.
Ma C, Huang C (2004) Experimental whole-field interferometry for transverse vibration of plates. J Sound Vib 271:493–506
290.
McComber P, Paradis A (1998) A cable galloping model for thin ice accretions. Atmos Res 46:13–25
291.
McConnell KG, Chang CN (1986) A study of the axial-torsional coupling effect on a sagged transmission line. Exp Mech 26:324–328
292.
Magnus W, Winkler DT (1966) Hill’s equation. Wiley-Interscience, New York
293.
Mailybaev AA, Yabuno H, Kaneko H (2004) Optimal shapes of parametrically excited beams. Struct Multidisciplinary Optim 27(6):435–445MathSciNet
294.
Makhecha DP, Ganapathi M, Patel BP (2001) Dynamic analysis of laminated composite plates subjected to thermal/mechanical loads using an accurate theory. Compos Struct 51:221–236
295.
Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Englewood Ciffs
296.
Mannini C, Bartoli G, Borri C, Borsani A, Ferrucci M, Procino L (2009) Recent developments in measurement and identification of bridge deck flutter derivatives. U. Peil, ed., WtG Berichte Nr. 11 - Windingenieurwesen in Forschung und Praxis, Dreiländertagung D-A-CH, Braunschweig, Germany, 1–15
297.
Marzocca P, Librescu L, Silva WA (2002) Flutter, postflutter, and control of a supersonic wing section. J Guid Contr Dynam 25:962–970
298.
Marzouk OA, Nayfeh AH, Arafat HN, Akhtar I (2007) Modeling steady-state and transient forces on a cylinder. J Vib Control 13:1065–1091
299.
Marzouk OA, Nayfeh AH (2009) Reduction of the loads on a cylinder undergoing harmonic in-line motion. Phys Fluids 21:083103-13
300.
Marzouk OA, Nayfeh AH (2010) Characterization of the flow over a cylinder moving harmonically in the cross-flow direction. Int J Non Linear Mech 45:821–833
301.
Masri SF (1975) Forced vibration of the damped bilinear hysteretic oscillator. J Acoust Soc Am 57:106–111
302.
Matsunaga H (1994) Free vibration and stability of thick elastic plates subjected to in-plane forces. Int J Solids Struct 31(22):3113–3124
303.
Matsunaga H (1997) Buckling instabilities of thick elastic plates subjected to in-plane stresses. Compos Struct 62(1):205–214MathSciNet
304.
Matsunaga H (2000) Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Compos Struct 48(4):231–244
305.
Matsunaga H (2001) Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses. Int J Mech Sci 43:1925–1944
306.
Matsunaga, H (2002) Vibration of cross-ply laminated composite plates subjected to initial in-plane stresses. Thin Wall Struct 40:557–571
307.
Matsunaga H (2006) Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory. Compos Struct 72:177–192
308.
Matsunaga H (2007) Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading. Compos Struct 77:249–262
309.
MATHEMATICA (2007) Wolfram Research Inc. Urbana Champaign, IL
310.
McKenna PJ, Walter W (1987) Nonlinear oscillations in a suspension bridge. Arch Rat Mech Anal 98:167–177MathSciNet
311.
McLachlan NW (1962) Theory and application of mathieu functions. Dover, New York
312.
Meirovitch L (1970) Methods of analytical dynamics. Mc-Graw-Hill, New York
313.
Melan J (1853) Theorie der eisernen bogenbrücken und der hangebrücken. Leipzig. (1913) Theory of arches and suspension bridges. Translated by D B Steinman, Myron C. Clark, Chicago
314.
Melde W (1859) Über Erregung stehender Wellen eines fadenförmigen Körpers. Ann Phys Chem 109:193–215
315.
Mathieu E (1868) Mémoire sur le movement vibratoire d’une membrane de forme elliptique. J Math Pures Appl 137–203
316.
Mettler E (1962) Dynamic buckling. In: Flugge (ed) Handbook of engineering mechanics. McGraw-Hill, New York
317.
Mikhlin SG (1964) Variational methods in mathematical physics. Pergamon, Oxford
318.
Miles J (1985) Parametric excitation of an internally resonant double pendulum. Z Angew Math Phys 36:337–345MathSciNet
319.
Mindlin RD (1951) Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. NASA Technical Paper 1903, Hampton, VA
320.
Mindlin RD (1951) Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech 38:31–38
321.
Mishra SS, Kumar K, Krishna P (2008) Multimode flutter of long-span cable-stayed bridge based on 18 experimental aeroelastic derivatives. J Wind Eng Ind Aerodyn 96:83–102
322.
Mittelmann HD, Roose D (eds) (1990) Continuation techniques and bifurcation problems, vol 92. ISNM, Birkhäuser
323.
Miyata T (2003) Historical view of long-span bridge aerodynamics. J Wind Eng Ind Aerodyn 91:1393–1410
324.
Mohr GA (1992) Finite elements for solids, fluids and optimization. Oxford University Press, Oxford
325.
Moisseiff LS, Leinhard, F (1933) Suspension bridges under the action of lateral forces, with discussion. Trans Am Soc Civ Eng 98:1080–1141
326.
Moon FC (2004) Chaotic vibrations. Wiley, New York
327.
Morley A (1917) Critical loads for long tapering struts. Engineering 104:295
328.
Murdock JA (1991) Perturbations. Wiley, New York
329.
Naghdi PM (1972) The theory of shells and plates. In Truesdell S (ed) Flügges Encyclopedia of Physics, vol VI a/2. Springer, New York, pp 425–640
330.
Nayfeh AH (1973) Perturbation methods. Wiley, New York
331.
Nayfeh AH, Mook DT, Lobitz DW (1974) Numerical-perturbation method for the nonlinear analysis of structural vibrations. AIAA J 12:1222–1228
332.
Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York
333.
Nayfeh AH (1981) Introduction to perturbation techniques. Wiley, New York
334.
Nayfeh AH, Pai PF (1989) Non-linear non-planar parametric responses of an inextensional beam. Int J Non Lin Mech 24(2):139–158
335.
Nayfeh AH, Balachandran B (1995) Applied nonlinear dynamics. Wiley-Interscience, New York
336.
Nayfeh AH, Lacarbonara W (1998) On the discretization of spatially continuous systems with quadratic and cubic nonlinearities. JSME Int J C-Dyn Con 41:510–531
337.
Nayfeh AH (2000) Nonlinear interactions. analytical, computational, and experimental methods. Wiley-Interscience, New York
338.
Nayfeh AH, Arafat H, Chin, CM, Lacarbonara W (2002) Multimode interactions in suspended cables. J Vib Control 8:337–387MathSciNet
339.
Nayfeh AH, Pai PF (2004) Linear and nonlinear structural mechanics. Wiley, New York
340.
Nayfeh AH, Arafat HN (2005) Nonlinear dynamics of closed spherical shells, Paper. No. DETC2005-85409. In: Proceedings of the 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, Sept. 25–28
341.
Navier CLMHL (1823) Rapport et mémoire sur le ponts suspendus. Paris, Imprimerie Royale
342.
Nazmy AS (1997) Stability and load-carrying capacity of three-dimensional long-span steel arch bridges. Comput Struct 65(6):857–868
343.
Nemat-Nasser S, Shatoff HD (1973) Numerical analysis of pre- and post-critical response of elastic continua at finite strains. Comput Struct 3:983–999
344.
Ng L, Rand RH (2002) Bifurcations in a Mathieu equation with cubic nonlinearities. Chaos Soliton Fract 14:173–181MathSciNet
345.
Noda N, Hetnarski RB, Tanigawa Y (2003) Thermal stresses, 2nd edn. Taylor & Francis, New York
346.
Noor, AK, Burton, WS (1989) Assessment of shear deformation theories for multilayered composite plates. Appl Mech Rev 42(1):1–13
347.
Nosier A, Kapania RK, Reddy JN (1993) Free vibration analysis of laminated plates using a layer-wise theory. AIAA J 31(12):2335–2346
348.
Pagano NJ (1969) Exact solutions for composite laminates in cylindrical bending. J Compos Mater 3:398–411
349.
Pagano NJ (1970) Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 4:20–34
350.
Pagano NJ, Hatfield SJ (1972) Elastic behavior of multi-layered bidirectional composites. AIAA J 10:931–933
351.
Paolone A, Vasta M, Luongo A (2006) Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces I. Non-linear model and stability analysis. Int J Non Linear Mech 41:586–594
352.
Pandya BN, Kant T (1988) Flexural analysis of laminated composites using refined higher-order C 0 plate bending elements. Comput Method Appl M 66:173–198
353.
Pasca M, Pignataro M, Luongo A (1991) Three-dimensional vibrations of tethered satellite system. J Contr Guid 14(2):312–320
354.
Pasca M, Vestroni F, Luongo A (1996) Stability and bifurcations of transversal motions of an orbiting string with a longitudinal force. Appl Math Mech ZAMM 76(4):337–340
355.
Pasquali M (2010) Geometrically exact models of thin plates towards nonlinear dynamic system identification via higher-order spectral approach. MS Thesis. Sapienza University of Rome
356.
Pasquali M, Lacarbonara W, Marzocca P (2011) System identification of plates using higher-order spectra: numerical and experimental investigations. Paper No. 945175, 52nd AIAA/ASME/ASCE/AHS Structures, Structural Dynamics & Materials Conference, Denver, CO, April 4–7
357.
Pasquali M, Lacarbonara W, Marzocca P (2011) Advanced system identification of plates using a higher-order spectral approach: theory and experiment. Paper no. DETC2011-47975, 2011 ASME DETC, Washington DC, August 28–31
358.
Patil MJ, Hodges D (2004) On the importance of aerodynamic and structural geometrical nonlinearities in aeroelastic behavior of high-aspect-ratio wings. J Fluid Struct 19:905–915
359.
Pellicano F, Amabili M (2006) Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads. J Sound Vib 293:227–252
360.
Petrangeli MP and Associates (2008) Ponte della Musica: Verifica delle strutture in acciaio dell’arco, dell’impalcato e della soletta. codifica E281004300SXA, Rome
361.
Petrolito J (1998) Approximate solutions of differential equations using Galerkin’s method and weighted residuals. Int J Mech Eng Educ 28:14–26
362.
Picone M (1928) Sul metodo delle minime potenze ponderate e sul metodo di Ritz per il calcolo approssimato nei problemi della fisica-matematica. Rend Circ Mat Palermo 52: 225–253
363.
Pignataro M, Rizzi N, Luongo A (1990) Bifurcation, stability and postcritical behaviour of elastic structures. Elsevier Science Publishers, Amsterdam
364.
Pilipchuk VN, Ibrahim RA (1999) Non-linear modal interactions in shallow suspended cables. J Sound Vib 227:1–28
365.
Pfeil MS, Batista RC (1995) Aerodynamic stability analysis of cable-stayed bridges. J Struct Eng-ASCE 121:1748–1788
366.
Podio-Guidugli P, Virga EG (1987) Transversely isotropic elasticity tensors. Proc R Soc London, Ser A 411:85–93MathSciNet
367.
Podio-Guidugli P (1989) An exact derivation of the thin plate equation. J Elast 22:121–133MathSciNet
368.
Preidikman S, Mook DT (1997) A new method for actively suppressing flutter of suspension bridges J Wind Eng Ind Aerodyn 69/71:955–974
369.
Preidikman S, Mook DT (1998) On the development of a passive-damping system for wind-excited oscillations of long span bridges J Wind Eng Ind Aerodyn 77/78:443–456
370.
Proceedings (1995) of the 4th International Conference on Tethers in Space, April 10–14, Washington DC
371.
Pugsley A (1968) The theory of suspension bridges, 2d edn. Edward Arnold, London
372.
Pugno N, Schwarzbart M, Steindl A, Troger H (2009) On the stability of the track of the space elevator. Acta Astronautica 64:524–537
373.
Quarteroni A, Sacco, R, Saleri, F (2007) Numerical mathematics. Springer, Berlin
374.
Ramania DV, Keitha WL, Rand RH (2004) Perturbation solution for secondary bifurcation in the quadratically-damped Mathieu equation. Int J Non Lin Mech 39:491–502
375.
Rand RH (1996) Dynamics of a nonlinear parametrically-excited PDE: 2-term truncation. Mech Res Commun 23:283–289MathSciNet
376.
Rand RH, Armbruster D (1987) Perturbation methods, bifurcation theory, and computer algebra. Springer, New York
377.
Reddy JN (1984) A simple higher-order theory for laminated composite plates. Trans ASME J Appl Mech 51:745–752
378.
Reddy JN (2004) Mechanics of laminated composite plates and shells, 2nd edn. CRC Press, Boca Raton, FL
379.
Rega G, Lacarbonara W, Nayfeh AH (2000) Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature. Solid mechanics and its applications vol 77. Kluwer, Dordrecht, p 235
380.
Rega G (2004) Nonlinear vibrations of suspended cables - Part I: Modeling and analysis. Part II: Deterministic phenomena. Appl Mech Rev 57:443–479
381.
Rega G, Lacarbonara W, Nayfeh AH, Chin CM (1999) Multiple resonances in suspended cables: direct versus reduced-order models. Int J Non Linear Mech 34:901–924
382.
Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech 12:69–77MathSciNet
383.
Ricks E (1979) An incremental approach to the solution of snapping and buckling problems. Int J Solids Struct 15:529–551
384.
Rodrigues O (1840) Des lois géometriques qui régissent les déplacements d’un systeme solide dans l’espace. J de Math (Liouville) 5:380–440
385.
Sabzevari A, Scanlan RH (1968) Aerodynamic instability of suspension bridges. J Eng Mech-ASCE 94:489–517
386.
Saito H, Sato K, Otomi K (1976) Nonlinear forced vibrations of a beam carrying concentrated mass under gravity. J Sound Vib 46(4):515–525
387.
Salinger AG, Burroughs EA, Pawlowski RP, Phipps ET, Romero LA (2005) Bifurcation tracking algorithms and software for large scale applications. J Bifur Chaos Appl Sci Engrg 15(3):1015–1032MathSciNet
388.
Salvatori L, Borri C (2007) Frequency- and time-domain methods for the numerical modeling of full-bridge aeroelasticity. Comput Struct 85:675–687
389.
Sanders JA, Verhulst F, Murdock J (2007) Averaging methods in nonlinear dynamical systems, 2nd edn. Springer, New York
390.
Sanjuán MAF (1998) Using nonharmonic forcing to switch the periodicity in nonlinear systems. Phys Rev E 58:4377–4382MathSciNet
391.
Sarkar PP, Caracoglia L, Haan FL, Sato H, Murakoshid J (2009) Comparative and sensitivity study of flutter derivatives of selected bridge deck sections. Part 1: Analysis of inter-laboratory experimental data. Eng Struct 31:158–169
392.
Sartorelli JC, Lacarbonara W (2012) Parametric resonances in a base-excited double pendulum, Nonlinear Dynam 69:1679–1692MathSciNet
393.
Scanlan RH (1987) Interpreting aeroelastic models of cable-stayed bridges. J Eng Mech-ASCE 113:555–575
394.
Sears A, Batra RC (2004) Macroscopic properties of carbon nanotubes from molecular-mechanics simulations. Phys Rev B 69:235406-10
395.
Seyranian AP, Yabuno H, Tsumoto K (2005) Instability and periodic motion of a physical pendulum with a vibrating suspension point (theoretical and experimental approach). Dokl Phys 50(9):467–472MathSciNet
396.
Somnay R, Ibrahim RA, Banasik RC (2006) Nonlinear dynamics of a sliding beam on two isolators. J Vib Control 12:685–712
397.
Strømmen E, Hjoorth-Hansen E (1995) The buffeting wind loading of structural members at an arbitrary attitude in the flow. J Wind Eng Ind Aerodyn 56:267–290
398.
Scanlan RH, Tomko JJ (1971) Airfoil and bridge deck flutter derivates. J Eng Mech-ASCE 97:1717–1737
399.
Selberg A (1961) Oscillation and aerodynamic stability of suspension bridges. Acta Polytechnica Scandinavia 308
400.
Seydel R (1994) Practical bifurcation and stability analysis. From equilibrium to chaos, 2nd edn. Springer, New York
401.
Seyranian AP (2001) Regions of resonance for Hill’s equation with damping. Dokl Ross Akad Nauk 376:44–47
402.
Shilov GE, Gurevich BL (1977) Integral, measure and derivative: a unified approach. In: Silverman RA (ed) Dover books on advanced mathematics. Dover Publications, New York
403.
Shufrin I, Rabinovitch O, Eisenberger M (2009) Elastic nonlinear stability analysis of thin rectangular plates through a semi-analytical approach. Int J Solids Struct 46:2075–2092
404.
Simo JC (1985) A finite strain beam formulation. The three-dimensional dynamical problem. Part I. Comput Method Appl M 49:55–70
405.
Simo JC, Marsden JE, Krishnaprasad PS (1988) The Hamiltonian structure of nonlinear elasticity: the material and convective representations of solids, rods and plates. Arch Ration Mech Anal 104:125–183MathSciNet
406.
Simiu E, Scanlan R (1996) Wind effects on structures. Fundamentals and applications to design, 3rd edn. Wiley-Interscience Publication, New York
407.
Skeldon AC (1994) Dynamics of a parametrically excited double pendulum. Phys D 75: 541–558MathSciNet
408.
Skop RA, Griffin OM (1973) A model for the vortex-excited resonant response of bluff cylinders. J Sound Vib 27:225–233
409.
Smith HJ, Blackburn JA, Grnbech-Jensen N (1992) Stability and Hopf bifurcations in an inverted pendulum. Am J Phys 60:903–908
410.
Stachowiak T, Okada T (2006) A numerical analysis of chaos in the double pendulum. Chaos Soliton Fract 29:417–422
411.
Stephenson A (1906) On a class of forced oscillations. Q J Math 37:353–360
412.
Stephenson A (1908) On a new type of dynamic stability. Mem Proc Manch Lit Phil Soc 52: 1–10
413.
Steinman DB (1934) A generalized deflection theory for suspension bridges. Trans Am Soc Civ Eng March:1133–1170
414.
Steinman DB (1946) Design of bridges against wind: V. Criteria for assuring aerodynamic stability. Civil Eng ASCE February:68–76
415.
Stevens KK (1966) On linear ordinary differential equations with periodic coefficients. SIAM J Appl Math 14:782–795MathSciNet
416.
Stojanovic R (1972) Nonlinear thermoelasticity. Springer, Wien
417.
Structural Engineers Association of California (1995) Performance-based seismic engineering of buildings. Vision 2000 Report. SEAOC Publications, Sacramento
418.
Strutt JWS (Lord Rayleigh) (1883) On maintained vibrations. Phil Mag 15:229–235
419.
Strutt JWS (Lord Rayleigh) (1887) On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure. Phil Mag 24:145–159
420.
Struble RA (1962) Nonlinear differential equations. McGraw-Hill, New York
421.
Sugimoto N (1981) Nonlinear theory for flexural motions of this elastic plate. J Appl Mech 48:377–382
422.
Synge JL, Chien WZ (1941) The intrinsic theory of elastic shells and plates. Theodore von Karman Anniversary Volume, California Institute of Technology, 103–120
423.
Tang DM, Dowell EH (2001) Experimental and theoretical study on aeroelastic response of high-aspect-ratio wings. AIAA J 39(8):1430–1441
424.
Tang DM, Dowell EH (2002) Experimental and theoretical study of gust response for high-aspect-ratio wing. AIAA J 40(3):419–429
425.
Tang DM, Dowell EH (2004) Effects of geometric structural nonlinearity on flutter and limit cycle oscillations of high-aspect-ratio wings. J Fluid Struct 19:291–306
426.
Task Committee on Cable-Suspended Structures (1977) Commentary on the tentative recommendations for cable-stayed bridge structures. J Struct Div Proc ASCE 103:941–959
427.
Theodorsen T (1931) On the theory of wing section with particular reference to the lift distribution. JNACA REPORT No. 383
428.
Theodorsen T (1931) Theory of wing section of arbitrary shape. JNACA REPORT No. 411
429.
Theodorsen T (1935) General theory of aerodynamic instability and the mechanism of flutter. JNACA REPORT No. 496
430.
Thompson JMT, Walker AC (1969) A general theory for the branching analysis of discrete structural systems. Int J Solids Struct 5:281–288
431.
Thompson JMT (1989) Chaotic phenomena triggering the escape from a potential well. Proc R Soc London, Ser A 421:195–225
432.
Timoshenko SP (1908) Buckling of bars of variable cross section. Bulletin of the Polytechnic Institute, Kiev, USSR
433.
Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill, New York
434.
Timoshenko SP, Young DH (1965) Theory of structures, 2nd edn. McGraw-Hill, New York
435.
Troger H, Steindl A (1991) Nonlinear stability and bifurcation theory. Springer, Wien
436.
Triantafyllou MS, Howell CT (1994) Dynamic response of cables under negative tension: an ill-posed problem. J Sound Vib 173:433–447
437.
Truesdell C (1954) A new chapter in the theory of the elastica. In Proc. 1st Midwestern Conf. Solid Mech. 52–54
438.
Trusdell C, Toupin RA (1960) The classical field theories. In: Flugge S (ed) Encyclopedia of physics, vol III/1. Springer, Berlin, pp 226–793
439.
Truesdell C, Noll N (1965) The nonlinear field theories of mechanics. In: Flügge S (ed) Handbuch der Physik, Band vol III/3. Springer, Berlin
440.
Tuc̆ková M, Tuc̆ek J,, Tuc̆ek P, Kubác̆ek L (2011) Experimental design of hysteresis loop measurements of nanosized ε-Fe2O3/SiO3 A statistically-based approach towards precise evaluation of ε-Fe2O3/SiO3 hysteresis loop parameters. In: NanoCon 2011, Sept 21–23, Brno, Czech Republic
441.
Ukeguchi N, Sakata H, Nishitani H (1966) An investigation of aeroelastic instability of suspension bridges. Int. Symp. on Suspension Bridges, Lisbon, Paper No. 11, 79–100
442.
UNI EN 1991-1-7: Part 1-7: Azioni in generale - Azioni eccezionali (2006)
443.
UNI EN 1991-2: Part 2: Carichi da traffico sui ponti (2005)
444.
van der Pol B (1927) On relaxation-oscillations. London Edinburgh Dublin Phil Mag J Sci 2(7):978–992
445.
Vaziri HH, Xie J (1992) Buckling of columns under variably distributed asial loads. Comput Struct 45:505–509
446.
Verhulst F (1990) Nonlinear differential equations and dynamical systems. Springer, Berlin
447.
Vestroni F, Luongo A, Pasca M (1995) Stability and control of transversal oscillations of a tethered satellite system. Appl Math Comp 70(2):343–360MathSciNet
448.
Vestroni F, Lacarbonara W, Carpineto N (2011) Hysteretic tuned-mass damper device (TMD) for passive control of mechanical vibrations, Italian Patent
449.
Vijayaraghavan A, Evan-Iwanowski RM (1967) Parametric instability of circular cylindrical shells. J Appl Mech 985–990
450.
Villaggio P (1997) Mathematical models for elastic structures. Cambridge University Press, Cambridge
451.
Visintin A (1994) Differential models of hysteresis. Springer, Berlin
452.
Vlasov VZ (1959) Thin-walled elastic bars (in Russian), 2nd edn. Fizmatgiz, Moscow
453.
von Kármán T (1910) Festigkeitsproblem im Maschinenbau. Encyk D Math Wiss IV:311–385
454.
Waisman H, Montoya A, Betti R, Noyan IC (2011) Load transfer and recovery length in parallel wires of suspension bridge cables. J Eng Mech-ASCE 137:227–237
455.
Walker AC (1969) A method of solution for nonlinear simultaneous algebraic equations. Int J Numer Methods Eng 1:197–180
456.
Walker AC (1969) A nonlinear finite ekment analysis of shallow circular arches. Int J Solids Struct 5:97–107
457.
Wang CM, Wang CY, Reddy JN (2005) Exact solutions for buckling of structural members. CRC Press, Boca Raton
458.
Weiyi C (1999) Derivation of the general form of elasticity tensor of the transverse isotropic material by tensor derivate. Appl Math Mech 20(3):309–314MathSciNet
459.
Wen RK, Medallah K (1987) Elastic stability of deck-type arch bridges. J Struct Eng ASCE 113(4):757–768
460.
Wenbin YuW, Kimb JS, Hodges DH, Chod M (2008) A critical evaluation of two Reissner–Mindlin type models for composite laminated plates. Aerospace Sci Technol 12(5):408–417
461.
Whitney JM, Pagano NJ (1970) Shear deformation in heterogeneous anisotropic plates. J Appl Mech 37:1031–1036
462.
Wilcox B, Dankowicz H (2009) Design of limit-switch sensors based on discontinuity-induced nonlinearities. In: Proceedings of IDETC/CIE 2009, San Diego, CA
463.
Wilcox B, Dankowicz H, Lacarbonara W (2009) Response of electrostatically actuated flexible MEMS structures to the onset of low-velocity contact. In: Proceedings of IDETC/CIE 2009, San Diego, CA
464.
Wu Q, Takahashi K, Nakamura S (2003) The effect of cable loosening on seismic response of a prestressed concrete cable-stayed bridge. J Sound Vib 268:71–84
465.
Wu W, Takahashi K, Nakamura S (2003) Non-linear vibrations of cables considering loosening. J Sound Vib 261:385–402
466.
Wu Q, Takahashi K, Nakamura S (2004) Non-linear response of cables subject to periodic support excitation considering cable loosening. J Sound Vib 271:453–463
467.
Wu Q, Takahashi K, Nakamura S (2007) Influence of cable loosening on nonlinear parametric vibrations of inclined cables. Struct Eng Mech 25
468.
Yabuno H (1994) Nonlinear stability analysis for summed-type combination resonance under parametrical excitation (application of center manifold theory and Grobner basis with computer algebra). Nippon Kikai Gakkai Ronbunshu C Hen/Trans Jpn Soc Mech Eng C 60(572): 1151–1158
469.
Yabuno H (1996) Buckling of a beam subjected to electromagnetic force and its stabilization by controlling the perturbation of the bifurcation. Nonlinear Dynam 10(3):271–285
470.
Yabuno H, Ide Y, Aoshima N (1998) Nonlinear analysis of a parametrically excited cantilever beam: (Effect of the tip mass on stationary response). JSME International Journal Series C: Dynamics, Control, Robotics, Design and Manufacturing 41(3):555–562
471.
Yabuno H, Nayfeh AH (2001) Nonlinear normal modes of a parametrically excited cantilever beam. Nonlin Dyn 25:65–77MathSciNet
472.
Yabuno H, Saigusa S, Aoshima N (2001) Stabilization of the parametric resonance of a cantilever beam by bifurcation control with a piezoelectric actuator. Nonlinear Dynam 26(2):143–161
473.
Yabuno H, Okhuma M, Lacarbonara W (2003) An experimental investigation of the parametric resonance in a buckled beam, Paper VIB-48615, 19th ASME Biennial Conf. on Mechanical Vibration and Noise
474.
Yabuno H, Kanda R, Lacarbonara W, Aoshima N (2004) Nonlinear active cancellation of the parametric resonance in a magnetically levitated body. J Dyn Syst Meas Contr Tran ASME 126(3):433–442
475.
Yabuno H, Murakami T, Kawazoe J, Aoshima N (2004) Suppression of parametric resonance in cantilever beam with a pendulum (Effect of static friction at the supporting point of the pendulum). J Vib Acoust 126(1):149–162
476.
Yakubovich VA, Starzhinskii VM (1975) Linear differential equations with periodic coefficients, vol 2. Wiley, New York
477.
Yu P, Desai YM, Shah AH, Popplewell N (1992) Three-degree-of-freedom model for galloping. Part I: Formulation. J Eng Mech-ASCE 119:2404–2424
478.
Yu P, Desai YM, Popplewell N, Shah AH (1992) Three-degree-of-freedom model for galloping. Part II: Solutions. J Eng Mech-ASCE 119:2426–2446
479.
Yu P, Bi Q (1998) Analysis of non-linear dynamics and bifurcations of a double pendulum. J Sound Vib 217:691–736MathSciNet
480.
Yu W (2005) Mathematical construction of a Reissner–Mindlin plate theory for composite laminates. Int J Solids Struct 42:6680–6699
481.
Zavodney LD, Nayfeh AH (1989) The non-linear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment. Int J Non Lin Mech 24:105–125
482.
Zhang X, Sun B, Peng W (2003) Study on flutter characteristics of cable-supported bridges. J Wind Eng Ind Aerodyn 91:841–854
483.
Zhang X, Sun B (2004) Parametric study on the aerodynamic stability of a long-span suspension bridge. J Wind Eng Ind Aerodyn 92:431–439
484.
Zhang X (2007) Influence of some factors on the aerodynamic behavior of long-span suspension bridges. J Wind Eng Ind Aerodyn 95:149–164
485.
Zhen W, Wanji C (2007) Buckling analysis of angle-ply composite and sandwich plates by combination of geometric stiffness matrix. Comput Mech 39:839–848
486.
Zhen W, Wanji C (2006) Free vibration of laminated composite and sandwich plates using global-local higher-order theory. J Sound Vib 298:333–349
487.
Ziegler SW, Cartmell MP (2001) Using motorized tethers for payload orbital transfer. J Spacecraft Rockets 38:904–913
488.
Zienkiewicz OC, Morgan K (1983) Finite elements and approximations. Wiley-Interscience, New York
Metadaten
Titel
The Nonlinear Theory of Arch-Supported Structures
verfasst von
Walter Lacarbonara
Copyright-Jahr
2013
Verlag
Springer US
Buch
Nonlinear Structural Mechanics

Print ISBN: 978-1-4419-1275-6

Electronic ISBN: 978-1-4419-1276-3

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4419-1276-3_10

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise