Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Dynamical Integrity: Three Decades of Progress from Macro to Nanomechanics Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Dynamical Integrity: A Novel Paradigm for Evaluating Load Carrying Capacity

Authors : Giuseppe Rega, Stefano Lenci, Laura Ruzziconi

Published in: Global Nonlinear Dynamics for Engineering Design and System Safety

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The chapter offers an overview of the effects of the research advancements in nonlinear dynamics on the evaluation of system safety. The achievements developed over the last 30 years entailed a substantial change of perspective. After recalling the outstanding contributions due to Euler and Koiter, we focus on Thompson’s intuition of global safety. This concept represents a paramount enhancement, full of theoretical and practical implications. Its relevance as a novel paradigm for evaluating the load carrying capacity of a system is highlighted. Making reference to a variety of different case studies, we emphasize that global safety has induced a deep development in the analysis, control, and design of mechanical and structural systems. Recent results are presented, and the possibility to implement effective dedicated control procedures based on global safety concepts is explored. We stress the importance of global safety for valorizing all the potential of the system and guaranteeing superior targets. The very general character of the dynamical integrity approach to design is highlighted.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now
previous chapter Dynamical Integrity: Three Decades of Progress from Macro to Nanomechanics
next chapter Interpreting and Predicting Experimental Responses of Micro- and Nano-Devices via Dynamical Integrity
Literature
Alsaleem, F. M., Younis, M. I., & Ruzziconi, L. (2010). An experimental and theoretical investigation of dynamic pull-in in MEMS resonators actuated electrostatically. Journal of Microelectromechanical Systems, 19(4), 794–806.CrossRef
Awrejcewicz, J., & Lamarque, C.-H. (2003). Bifurcation and chaos in nonsmooth mechanical systems. Singapore: World Scientific.CrossRef
Bazant, Z., & Cedolin, L. (1991). Stability of structures. New York: Oxford University Press.MATH
Belardinelli, P., & Lenci, S. (2016a). A first parallel programming approach in basins of attraction computation. International Journal of Non-Linear Mechanics, 80, 76–81.CrossRef
Belardinelli, P., & Lenci, S. (2016b). An efficient parallel implementation of cell mapping methods for MDOF systems. Nonlinear Dynamics, 86(4), 2279–2290.MathSciNetCrossRef
Belardinelli, P., Lenci, S., & Rega, G. (2018). Seamless variation of isometric and anisometric dynamical integrity measures in basins’ erosion. Communications in Nonlinear Science and Numerical Simulation, 56, 499–507.MathSciNetCrossRef
Bishop, S. R., & Clifford, M. J. (1996). Zones of chaotic behavior in the parametrically excited pendulum. Journal of Sound and Vibration, 189, 142–147.MathSciNetCrossRef
Budiansky, B., & Hutchinson, J. W. (1964). Dynamics buckling of imperfection-sensitive structures. In Proceedings of the Eleventh International Congress of Applied Mechanics, Munich, Germany (pp. 636–651).
Das, S., & Wahi, P. (2016). Initiation and directional control of period-1 rotation for parametric pendulum. Proceedings of the Royal Society of London A, 472, 20160719.MathSciNetCrossRef
de Souza Jr, J. R., & Rodrigues, M. L. (2002). An investigation into mechanisms of loss of safe basins in a 2 D.O.F. nonlinear oscillator. Journal of the Brazilian Society of Mechanical Sciences, 24, 93–98.CrossRef
Eason, R., & Dick, A. J. (2014). A parallelized multi-degrees-of-freedom cell map method. Nonlinear Dynamics, 77(3), 467–479.CrossRef
Euler, L. (1744). Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Isoperimetrici Latissimo Sensu Accepti, Addentamentum 1: de Curvis Elasticis. Laussanae et Genevae, Apud Marcum-Michaelem, Bousquet et Socios.
Gan, C. B., & He, S. M. (2007). Studies on structural safety in stochastically excited Duffing oscillator with double potential wells. Acta Mechanica Sinica, 23(5), 577–583.MathSciNetCrossRef
Gonçalves, P. B., & Del Prado, Z. J. G. N. (2002). Nonlinear oscillations and stability of parametrically excited cylindrical shells. Meccanica, 37, 569–597.CrossRef
Gonçalves, P. B., & Del Prado, Z. J. G. N. (2005). Low-dimensional Galerkin models for nonlinear vibration and instability analysis of cylindrical shells. Nonlinear Dynamics, 41, 129–145.MathSciNetCrossRef
Gonçalves, P. B., Orlando, D., Lenci, S., & Rega, G. (2018). Nonlinear dynamics, safety and control of structures liable to interactive unstable buckling. In S. Lenci & G. Rega (Eds.), Global nonlinear dynamics for engineering design and system safety (Vol. 588, pp. 167–228). CISM Courses and Lectures. Cham: Springer.
Gonçalves, P. B., & Santee, D. (2008). Influence of uncertainties on the dynamic buckling loads of structures liable to asymmetric post-buckling behavior. Mathematical Problems in Engineering, 2008, 490137-1–490137-24.
Gonçalves, P. B., Silva, F. M. A., & Del Prado, Z. J. G. N. (2007). Global stability analysis of parametrically excited cylindrical shells through the evolution of basin boundaries. Nonlinear Dynamics, 50, 121–145.MathSciNetCrossRef
Gonçalves, P. B., Silva, F. M. A., Rega, G., & Lenci, S. (2011). Global dynamics and integrity of a two-dof model of a parametrically excited cylindrical shell. Nonlinear Dynamics, 63, 61–82.MathSciNetCrossRef
Grebogi, C., Ott, E., & Yorke, J. A. (1983). Crises, sudden changes in chaotic attractors and transient chaos. Physica D: Nonlinear Phenomena, 7, 181–200.MathSciNetCrossRef
Guckenheimer, J., & Holmes, P. J. (1983). Nonlinear oscillations, dynamical systems and bifurcation of vector fields. New York: Springer.CrossRef
Hong, L., & Sun, J. (2006). Bifurcations of a forced Duffing oscillator in the presence of fuzzy noise by the generalized cell mapping method. International Journal of Bifurcation and Chaos, 16(10), 3043–3051.CrossRef
Housner, G. W. (1963). The behaviour of inverted pendulum structures during earthquakes. Bulletin of the Seismological Society of America, 53(2), 403–417.
Hsu, C. S. (1987). Cell to cell mapping: A method of global analysis for nonlinear system. New York: Springer.CrossRef
Hsu, C. S., & Chiu, H. M. (1987). Global analysis of a system with multiple responses including a strange attractor. Journal of Sound and Vibration, 114(2), 203–218.MathSciNetCrossRef
Kirkpatrick, P. (1927). Seismic measurements by the overthrow of columns. Bulletin of the Seismological Society of America, 17, 95–109.
Koch, B. P., & Leven, R. W. (1985). Subharmonic and homoclinic bifurcations in a parametrically forced pendulum. Physica D: Nonlinear Phenomena, 16, 1–13.MathSciNetCrossRef
Koh, A. S. (1986). Rocking of rigid blocks on randomly shaking foundations. Nuclear Engineering and Design, 97, 269–276.CrossRef
Koiter, W. T. (1945). Over de Stabiliteit van het Elastisch Evenwicht. Ph.D. Thesis, Delft University, Delft, The Netherlands. English translation: Koiter, W. T. (1967). On the stability of elastic equilibrium. NASA technical translation F-10, 833, Clearinghouse, US Department of Commerce/National Bureau of Standards N67–25033.
Kreuzer, E., & Lagemann, B. (1996). Cell mapping for multi-degree-of-freedom-systems parallel computing in nonlinear dynamics. Chaos, Solitons & Fractals, 7(10), 1683–1691.MathSciNetCrossRef
Kustnezov, Y. A. (1995). Elements of applied bifurcation theory. New York: Springer.
Lansbury, A. N., Thompson, J. M. T., & Stewart, H. B. (1992). Basin erosion in the twin-well Duffing oscillator: Two distinct bifurcation scenarios. International Journal of Bifurcation and Chaos, 2, 505–532.MathSciNetCrossRef
Leine, R. I. (2010). The historical development of classical stability concepts: Lagrange, Poisson and Lyapunov stability. Nonlinear Dynamics, 59, 173–182.MathSciNetCrossRef
Lenci, S., Brocchini, M., & Lorenzoni, C. (2012a). Experimental rotations of a pendulum on water waves. ASME Journal of Computational and Nonlinear Dynamics, 7(1), 011007-1–011007-9.CrossRef
Lenci, S., Orlando, D., Rega, G., & Gonçalves, P. B. (2012b). Controlling practical stability and safety of mechanical systems by exploiting chaos properties. Chaos, 22(4), 047502-1–047502-15.
Lenci, S., & Rega, G. (1998a). A procedure for reducing the chaotic response region in an impact mechanical system. Nonlinear Dynamics, 15, 391–409.MathSciNetCrossRef
Lenci, S., & Rega, G. (1998b). Controlling nonlinear dynamics in a two-well impact system. Part I. Attractors and bifurcation scenario under symmetric excitations. International Journal of Bifurcation and Chaos, 8, 2387–2408.MathSciNetCrossRef
Lenci, S., & Rega, G. (1998c). Controlling nonlinear dynamics in a two-well impact system. Part II. Attractors and bifurcation scenario under unsymmetric optimal excitations. International Journal of Bifurcation and Chaos, 8, 2409–2424.MathSciNetCrossRef
Lenci, S., & Rega, G. (2003a). Optimal control of homoclinic bifurcation: Theoretical treatment and practical reduction of safe basin erosion in the Helmholtz oscillator. Journal of Vibration and Control, 9, 281–315.MathSciNetMATH
Lenci, S., & Rega, G. (2003b). Optimal control of nonregular dynamics in a Duffing oscillator. Nonlinear Dynamics, 33, 71–86.MathSciNetCrossRef
Lenci, S., & Rega, G. (2003c). Optimal numerical control of single-well to cross-well chaos transition in mechanical systems. Chaos, Solitons & Fractals, 15, 173–186.MathSciNetCrossRef
Lenci, S., & Rega, G. (2004a). A dynamical systems analysis of the overturning of rigid blocks. In CD-Rom Proceedings of the XXI International Conference of Theoretical and Applied Mechanics, IPPT PAN, Warsaw, Poland, 15–21 August 2004. ISBN 83-89687-01-1.
Lenci, S., & Rega, G. (2004b). A unified control framework of the nonregular dynamics of mechanical oscillators. Journal of Sound and Vibration, 278(4–5), 1051–1080.MathSciNetCrossRef
Lenci, S., & Rega, G. (2004c). Global optimal control and system-dependent solutions in the hardening Helmholtz-Duffing oscillator. Chaos, Solitons & Fractals, 21, 1031–1046.MathSciNetCrossRef
Lenci, S., & Rega, G. (2004d). Numerical aspects in the optimal control and anti-control of rigid block dynamics. In Proceedings of the Sixth World Conference on Computational Mechanics, WCCM VI, Beijing, China, 5–10 September 2004.
Lenci, S., & Rega, G. (2005). Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks. International Journal of Bifurcation and Chaos, 15(6), 1901–1918.MathSciNetCrossRef
Lenci, S., & Rega, G. (2006a). A dynamical systems approach to the overturning of rocking blocks. Chaos, Solitons & Fractals, 28, 527–542.MathSciNetCrossRef
Lenci, S., & Rega, G. (2006b). Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam. Journal of Micromechanics and Microengineering, 16, 390–401.CrossRef
Lenci, S., & Rega, G. (2006c). Optimal control and anti-control of the nonlinear dynamics of a rigid block. Philosophical Transactions of the Royal Society A, 364, 2353–2381.MathSciNetCrossRef
Lenci, S., & Rega, G. (2008). Competing dynamic solutions in a parametrically excited pendulum: Attractor robustness and basin integrity. ASME Journal of Computational and Nonlinear Dynamics, 3, 041010-1–041010-9.CrossRef
Lenci, S., & Rega, G. (2011a). Experimental versus theoretical robustness of rotating solutions in a parametrically excited pendulum: A dynamical integrity perspective. Physica D: Nonlinear Phenomena, 240, 814–824.CrossRef
Lenci, S., & Rega, G. (2011b). Forced harmonic vibration in a Duffing oscillator with negative linear stiffness and linear viscous damping. In I. Kovacic & M. J. Brennan (Eds.), The Duffing equation: Nonlinear oscillators and their behaviour (pp. 219–276). Wiley.
Lenci, S., & Rega, G. (2011c). Load carrying capacity of systems within a global safety perspective. Part I. Robustness of stable equilibria under imperfections. International Journal of Nonlinear Mechanics, 46, 1232–1239.CrossRef
Lenci, S., & Rega, G. (2011d). Load carrying capacity of systems within a global safety perspective. Part II. Attractor/basin integrity under dynamic excitations. International Journal of Nonlinear Mechanics, 46, 1240–1251.CrossRef
Lenci, S., Rega, G., & Ruzziconi, L. (2013). Dynamical integrity as a conceptual and operating tool for interpreting/predicting experimental behavior. Philosophical Transactions of the Royal Society of London A, 371(1993), 20120423-1–20120423-19.
Lyapunov, A. M. (1892). The general problem of the stability of motion. Ph.D. Thesis, Moscow University, Moscow, Russia. English translation: Lyapunov, A. M. (1992). The general problem of the stability of motion. London: Taylor & Francis.
Mang, H. A., Jia, X., & Hoenger, G. (2009). Hilltop buckling as the A and Ω in sensitivity analysis of the initial postbuckling behavior of elastic structures. Journal of Civil Engineering and Management, 15, 35–46.CrossRef
Milne, J. (1881). Experiments in observational seismology. Transactions of the Seismological Society of Japan, 3, 12–64.
Moon, F. C. (1980). Experiments on chaotic motions of a forced nonlinear oscillator: Strange attractors. Journal of Applied Mechanics, 47(3), 638–644.CrossRef
Moon, F. C. (1992). Chaotic and fractal dynamics. An introduction for applied scientists and engineers. New York: Wiley.
Nayfeh, A. H., & Balachandran, B. (1995). Applied nonlinear dynamics. New York: Wiley.CrossRef
Novak, M. (1969). Aeroelastic galloping of prismatic bodies. ASCE Journal of the Engineering Mechanics Division, 95(1), 115–142.
Oppenheim, I. J. (1992). The masonry arch as a four-link mechanism under base motion. Earthquake Engineering and Structural Dynamics, 21, 1005–1017.CrossRef
Orlando, D., Gonçalves, P. B., Rega, G., & Lenci, S. (2011). Influence of modal coupling on the nonlinear dynamics of Augusti’s model. ASME Journal of Computational and Nonlinear Dynamics, 6, 041014-1–041014-11.CrossRef
Perry, J. (1881). Note on the rocking of a column. Transactions of the Seismological Society of Japan, 3, 103–106.
Pignataro, M., Rizzi, N., & Luongo, A. (1990). Stability, bifurcation and postcritical behaviour of elastic structures. Amsterdam: Elsevier Science Publishers.
Plaut, R. H., Fielder, W. T., & Virgin, L. N. (1996). Fractal behaviour of an asymmetric rigid block overturning due to harmonic motion of a tilted foundation. Chaos, Solitons & Fractals, 7, 177–196.CrossRef
Rainey, R. C. T., & Thompson, J. M. T. (1991). The transient capsize diagram—A new method of quantifying stability in waves. Journal of Ship Research, 35(1), 58–62.
Rega, G., & Lenci, S. (2003). Bifurcations and chaos in single-d.o.f. mechanical systems: Exploiting nonlinear dynamics for their control. In A. Luongo (Ed.), Recent research development in structural dynamics (pp. 331–369). Kerala: Research Signpost.
Rega, G., & Lenci, S. (2005). Identifying, evaluating, and controlling dynamical integrity measures in nonlinear mechanical oscillators. Nonlinear Analysis, 63, 902–914.MathSciNetCrossRef
Rega, G., & Lenci, S. (2008). Dynamical integrity and control of nonlinear mechanical oscillators. Journal of Vibration and Control, 14, 159–179, 2008.CrossRef
Rega, G., & Lenci, S. (2009). Recent advances in control of complex dynamics in mechanical and structural systems. In M. A. F. Sanjuan & C. Grebogi (Eds.), Recent progress in controlling chaos (pp. 189–237). Singapore: World Scientific.MATH
Rega, G., & Lenci, S. (2015). A global dynamics perspective for system safety from macro- to nanomechanics: Analysis, control, and design engineering. Applied Mechanics Reviews, 67, 050802-1–050802-19.
Rega, G., Lenci, S., & Thompson, J. M. T. (2010). Controlling chaos: The OGY method, its use in mechanics, and an alternative unified framework for control of non-regular dynamics. In M. Thiel, J. Kurths, M. C. Romano, G. Károlyi, & A. Moura (Eds.), Nonlinear dynamics and chaos: Advances and perspectives (pp. 211–269). Berlin, Heidelberg: Springer.CrossRef
Rega, G., & Settimi, V. (2013). Bifurcation, response scenarios and dynamic integrity in a single-mode model of noncontact atomic force microscopy. Nonlinear Dynamics, 73(1–2), 101–123.MathSciNetCrossRef
Ruzziconi, L., Bataineh, A. M., Younis, M. I., Cui, W., & Lenci, S. (2013a). Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: Experimental investigation and reduced-order modeling. Journal of Micromechanics and Microengineering, 23(7), 075012-1–075012-14.CrossRef
Ruzziconi, L., Lenci, S., & Younis, M. I. (2013b). An imperfect microbeam under an axial load and electric excitation: Nonlinear phenomena and dynamical integrity. International Journal of Bifurcation and Chaos, 23(2), 1350026-1–1350026-17.MathSciNetCrossRef
Ruzziconi, L., Lenci, S., & Younis, M. I. (2018). Interpreting and predicting experimental responses of micro and nano devices via dynamical integrity. In S. Lenci & G. Rega (Eds.), Global nonlinear dynamics for engineering design and system safety (Vol. 588, pp. 113–166). CISM Courses and Lectures. Cham: Springer.
Ruzziconi, L., Younis, M. I., & Lenci, S. (2012). An efficient reduced-order model to investigate the behavior of an imperfect microbeam under axial load and electric excitation. ASME Journal of Computational and Nonlinear Dynamics, 8, 011014-1–011014-9.
Ruzziconi, L., Younis, M. I., & Lenci, S. (2013c). An electrically actuated imperfect microbeam: Dynamical integrity for interpreting and predicting the device response. Meccanica, 48(7), 1761–1775.MathSciNetCrossRef
Ruzziconi, L., Younis, M. I., & Lenci, S. (2013d). Dynamical integrity for interpreting experimental data and ensuring safety in electrostatic MEMS. In M. Wiercigroch, & G. Rega (Eds.), IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design (Vol. 32, pp. 249–261). IUTAM Bookseries. Springer.
Ruzziconi, L., Younis, M. I., & Lenci, S. (2013e). Multistability in an electrically actuated carbon nanotube: a dynamical integrity perspective. Nonlinear Dynamics, 74(3), 533–549.
Ruzziconi, L., Younis, M. I., & Lenci, S. (2013f). Parameter identification of an electrically actuated imperfect microbeam. International Journal of Non-Linear Mechanics, 57, 208–219.CrossRef
Settimi, V., Gottlieb, O., & Rega, G. (2015). Asymptotic analysis of a noncontact AFM microcantilever sensor with external feedback control. Nonlinear Dynamics, 79(4), 2675–2698.MathSciNetCrossRef
Settimi, V., & Rega, G. (2016a). Exploiting global dynamics of a noncontact atomic force microcantilever to enhance its dynamical robustness via numerical control. International Journal of Bifurcation and Chaos, 26, 1630018-1–1630018-17.MathSciNetCrossRef
Settimi, V., & Rega, G. (2016b). Global dynamics and integrity in noncontacting atomic force microscopy with feedback control. Nonlinear Dynamics, 86(4), 2261–2277.CrossRef
Settimi, V., & Rega, G. (2016c). Influence of a locally-tailored external feedback control on the overall dynamics of a non-contact AFM model. International Journal of Non-Linear Mechanics, 80, 144–159.CrossRef
Settimi, V., & Rega, G. (2018). Local versus global dynamics and control of an AFM model in a safety perspective. In S. Lenci & G. Rega (Eds.), Global nonlinear dynamics for engineering design and system safety (Vol. 588, pp. 229–286). CISM Courses and Lectures. Cham: Springer.
Silva, F. M. A., & Gonçalves, P. B. (2015). The influence of uncertainties and random noise on the dynamic integrity analysis of a system liable to unstable buckling. Nonlinear Dynamics, 81(1–2), 707–724.CrossRef
Silva, F. M. A., Gonçalves, P. B., & Del Prado, Z. J. G. N. (2013). Influence of physical and geometrical system parameters uncertainties on the nonlinear oscillations of cylindrical shells. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 34, 622–632.
Soliman, M. S., & Gonçalves, P. B. (2003). Chaotic behavior resulting in transient and steady state instabilities of pressure-loaded shallow spherical shells. Journal of Sound and Vibration, 259(3), 497–512.CrossRef
Soliman, M. S., & Thompson, J. M. T. (1989). Integrity measures quantifying the erosion of smooth and fractal basins of attraction. Journal of Sound and Vibration, 135, 453–475.MathSciNetCrossRef
Soliman, M. S., & Thompson, J. M. T. (1990). Stochastic penetration of smooth and fractal basin boundaries under noise excitation. Dynamics and Stability of Systems, 5(4), 281–298.MathSciNetCrossRef
Soliman, M. S., & Thompson, J. M. T. (1991). Transient and steady state analysis of capsize phenomena. Applied Ocean Research, 13(2), 82–92.CrossRef
Soliman, M. S., & Thompson, J. M. T. (1992). Global dynamics underlying sharp basin erosion in nonlinear driven oscillators. Physical Review A, 45(6), 3425–3431.CrossRef
Sun, J. Q. (1994). Effect of small random disturbance on the ‘Protection Thickness’ of attractors of nonlinear dynamic systems. In J. M. T. Thompson & S. R. Bishop (Eds.), Nonlinearity and chaos in engineering dynamics (pp. 435–437). Chichester: Wiley.
Sun, J. Q. (2013). Control of nonlinear dynamic systems with the cell mapping method. In O. Schütze, C. A. Coello Coello, A.-A. Tantar, E. Tantar, P. Bouvry, & P. Del Moral (Eds.), EVOLVE—A bridge between probability, set oriented numerics, and evolutionary computation II. Advances in intelligent systems and computing (pp. 3–18). Berlin, Heidelberg: Springer.
Xiong, F. R., Han, Q., Hong, L., & Sun, J. Q. (2018). Global analysis of nonlinear dynamical systems. In S. Lenci & G. Rega (Eds.), Global nonlinear dynamics for engineering design and system safety (Vol. 588, pp. 287–318). CISM Courses and Lectures. Cham: Springer.
Sun, J. Q., & Hsu, C. S. (1991). Effects of small random uncertainties on the non-linear systems studied by the generalized cell mapping methods. Journal of Sound and Vibration, 147(2), 185–201.MathSciNetCrossRef
Szemplińska-Stupnicka, W. (1995). The analytical predictive criteria for chaos and escape in nonlinear oscillators: A survey. Nonlinear Dynamics, 7(2), 129–147.MathSciNetCrossRef
Szemplińska-Stupnicka, W., & Rudowski, J. (1993). Steady state in the twin-well potential oscillator: Computer simulations and approximate analytical studies. Chaos, 3, 375–385.CrossRef
Szemplińska-Stupnicka, W., Tyrkiel, E., & Zubrzycki, A. (2000). The global bifurcations that lead to transient tumbling chaos in a parametrically driven pendulum. International Journal of Bifurcation and Chaos, 10, 2161–2175.MathSciNetMATH
Thom, R. (1972). Structural stability and morphogenesis. Massachusetts: W.A. Benjamin Inc.
Thompson, J. M. T. (1982). Instability and catastrophe in science and engineering. Wiley.
Thompson, J. M. T. (1989). Chaotic phenomena triggering the escape from a potential well. Proceedings of the Royal Society of London A, 421, 195–225.MathSciNetCrossRef
Thompson, J. M. T. (1997). Designing against capsize in beam seas: Recent advances and new insights. Applied Mechanics Reviews, 50(5), 307–325.CrossRef
Thompson, J. M. T. (2018). Dynamical integrity: Three decades of progress from macro to nano mechanics. In S. Lenci & G. Rega (Eds.), Global nonlinear dynamics for engineering design and system safety (Vol. 588, pp. 1–26). CISM Courses and Lectures. Cham: Springer.
Thompson, J. M. T., & Hunt, G. W. (1973). A general theory of elastic stability. London: Wiley.MATH
Thompson, J. M. T., Rainey, R. C. T., & Soliman, M. S. (1990). Ship stability criteria based on chaotic transients from incursive fractals. Philosophical Transactions of the Royal Society of London A, 332(1624), 149–167.MathSciNetCrossRef
Thompson, J. M. T., & Soliman, M. S. (1990). Fractal control boundaries of driven oscillators and their relevance to safe engineering design. Proceedings of the Royal Society of London A, 428(1874), 1–13.CrossRef
Thompson, J. M. T., & Stewart, H. B. (1986). Nonlinear dynamics and chaos. Chichester: Wiley (second extended edition, 2002).
Thompson, J. M. T., & Ueda, Y. (1989). Basin boundary metamorphoses in the canonical escape equation. Dynamics and Stability of Systems, 4(3–4), 285–294.MathSciNetCrossRef
Troger, H., & Steindl, A. (1991). Nonlinear stability and bifurcation theory. Wien: Springer.CrossRef
van Campen, D. H., van de Vorst, E. L. B., van der Spek, J. A. W., & de Kraker, A. (1995). Dynamics of a multi-DOF beam system with discontinuous support. Nonlinear Dynamics, 8(4), 453–466.CrossRef
van der Heijden, A. M. A. (ed.). (2009). W. T. Koiter’s elastic stability of solids and structures. Cambridge University Press.
Wiercigroch, M. (2010). A new concept for energy extraction from waves via parametric pendulor. UK Patent Application.
Wiercigroch, M., & Pavlovskaia, E. (2008). Non-linear dynamics of engineering systems. International Journal of Non-Linear Mechanics, 43(6), 459–461.CrossRef
Wiercigroch, M., & Rega, G. (2013). Introduction to NDATED. In M. Wiercigroch & G. Rega (Eds.), IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design (Vol. 32, pp. v–viii). IUTAM Bookseries. Springer.
Wiggins, S. (1990). Introduction to applied nonlinear dynamical systems and chaos. New York, Heidelberg, Berlin: Springer.CrossRef
Winkler, T., Meguro, K., & Yamazaki, F. (1995). Response of rigid body assemblies to dynamic excitation. Earthquake Engineering and Structural Dynamics, 24, 1389–1408.CrossRef
Xu, T., Ruzziconi, L., & Younis, M. I. (2017). Global investigation of the nonlinear dynamics of carbon nanotubes. Acta Mechanica, 228(3), 1029–1043.MathSciNetCrossRef
Xu, X., Pavlovskaia, E., Wiercigroch, M., Romeo, R., & Lenci, S. (2007). Dynamic interactions between parametric pendulum and electrodynamical shaker. ZAMM—Journal of Applied Mathematics and Mechanics, 87, 172–186.MathSciNetCrossRef
Xu, X., & Wiercigroch, M. (2007). Approximate analytical solutions for oscillatory and rotational motion of a parametric pendulum. Nonlinear Dynamics, 47, 311–320.MathSciNetCrossRef
Xu, X., Wiercigroch, M., & Cartmell, M. P. (2005). Rotating orbits of a parametrically excited pendulum. Chaos, Solitons & Fractals, 23, 1537–1548.CrossRef
Younis, M. I. (2011). MEMS linear and nonlinear statics and dynamics. New York: Springer.CrossRef
Zeeman, E. C. (1977). Catastrophe theory: Selected papers, 1972–1977. Oxford, England: Addison-Wesley.MATH
Metadata
Title
Dynamical Integrity: A Novel Paradigm for Evaluating Load Carrying Capacity
Authors
Giuseppe Rega
Stefano Lenci
Laura Ruzziconi
Copyright Year
2019
Book
Global Nonlinear Dynamics for Engineering Design and System Safety

Print ISBN: 978-3-319-99709-4

Electronic ISBN: 978-3-319-99710-0

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-99710-0_2

Premium Partners

    Image Credits