Skip to main content
Erschienen in: Meccanica 11/2016

08.02.2016 | Nonlinear Dynamics, Identification and Monitoring of Structures

A comprehensive analysis of hardening/softening behaviour of shearable planar beams with whatever axial boundary constraint

verfasst von: S. Lenci, F. Clementi, G. Rega

Erschienen in: Meccanica | Ausgabe 11/2016

Einloggen

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

search-config
loading …

Abstract

The free nonlinear oscillations of a planar elastic beam are investigated based on a comprehensive asymptotic treatment of the exact equations of motion. With the aim of investigating the behaviour also for low slenderness, shear deformations and rotational inertia are taken into account. Attention is payed to the influence of the geometrical and mechanical parameters, and of the boundary conditions in changing the nonlinear behaviour from softening to hardening. An axial linear spring is added to one end of the beam, and it is shown how the behaviour changes qualitatively on passing from the hinged-hinged (commonly hardening) to the hinged-supported (commonly softening) case. Some interesting, and partially unexpected, results are obtained also for values of the slenderness moderately low but still in the realm of practical applications.

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!

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!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Atluri S (1973) Nonlinear vibrations of hinged beam including nonlinear inertia effects. ASME J Appl Mech 40:121–126MATH Atluri S (1973) Nonlinear vibrations of hinged beam including nonlinear inertia effects. ASME J Appl Mech 40:121–126MATH
2.
Zurück zum Zitat Luongo A, Rega G, Vestroni F (1986) On nonlinear dynamics of planar shear indeformable beams. ASME J Appl Mech 53:619–624MATH Luongo A, Rega G, Vestroni F (1986) On nonlinear dynamics of planar shear indeformable beams. ASME J Appl Mech 53:619–624MATH
3.
Zurück zum Zitat Kauderer H (1958) Nichtlinear mechanik. Springer, Berlin. ISBN: 978-3-642-92734-8MATH Kauderer H (1958) Nichtlinear mechanik. Springer, Berlin. ISBN: 978-3-642-92734-8MATH
4.
Zurück zum Zitat Crespo da Silva MRM (1988) Nonlinear flexural-flexural-torsional-extensional dynamics of beams. II. Response analysis. Int J Solids Struct 24:1235–1242MATH Crespo da Silva MRM (1988) Nonlinear flexural-flexural-torsional-extensional dynamics of beams. II. Response analysis. Int J Solids Struct 24:1235–1242MATH
5.
Zurück zum Zitat Mettler E (1962) Dynamic buckling. In: Flugge (ed) Handbook of engineering mechanics. McGraw-Hill, New York. ISBN: 0070213925 Mettler E (1962) Dynamic buckling. In: Flugge (ed) Handbook of engineering mechanics. McGraw-Hill, New York. ISBN: 0070213925
6.
Zurück zum Zitat Lacarbonara W, Yabuno H (2006) Refined models of elastic beams undergoing large in-plane motions: theory and experiments. Int J Solids Struct 43:5066–5084MATH Lacarbonara W, Yabuno H (2006) Refined models of elastic beams undergoing large in-plane motions: theory and experiments. Int J Solids Struct 43:5066–5084MATH
7.
Zurück zum Zitat Lacarbonara W (2013) Nonlinear structural mechanics. Springer, New York. ISBN: 978-1-4419-1276-3MATH Lacarbonara W (2013) Nonlinear structural mechanics. Springer, New York. ISBN: 978-1-4419-1276-3MATH
8.
Zurück zum Zitat Simo JC, Vu-Quoc L (1991) A geometrically-exact beam model incorporating shear and torsion warping deformation. Int J Solids Struct 27:371–393MATH Simo JC, Vu-Quoc L (1991) A geometrically-exact beam model incorporating shear and torsion warping deformation. Int J Solids Struct 27:371–393MATH
9.
Zurück zum Zitat Nayfeh AH, Pai PF (2004) Linear and nonlinear structural mechanics. Wiley, New York. ISBN: 978-0-471-59356-0MATH Nayfeh AH, Pai PF (2004) Linear and nonlinear structural mechanics. Wiley, New York. ISBN: 978-0-471-59356-0MATH
10.
Zurück zum Zitat Cao DQ, Tucker RW (2008) Nonlinear dynamics of elastic rods using the Cosserat theory: modelling and simulation. Int J Solids Struct 45:460–477MATH Cao DQ, Tucker RW (2008) Nonlinear dynamics of elastic rods using the Cosserat theory: modelling and simulation. Int J Solids Struct 45:460–477MATH
11.
Zurück zum Zitat Stoykov S, Ribeiro P (2010) Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross section: the influence of warping, shear deformation and longitudinal displacements. Int J Mech Sci 52:1505–1521 Stoykov S, Ribeiro P (2010) Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross section: the influence of warping, shear deformation and longitudinal displacements. Int J Mech Sci 52:1505–1521
12.
Zurück zum Zitat Luongo A, Zulli D (2013) Mathematical models of beams and cables. Wiley-ISTE, New York. ISBN: 978-1-84821-421-7MATH Luongo A, Zulli D (2013) Mathematical models of beams and cables. Wiley-ISTE, New York. ISBN: 978-1-84821-421-7MATH
13.
Zurück zum Zitat Formica G, Arena A, Lacarbonara W, Dankowicz H (2013) Coupling FEM with parameter continuation for analysis and bifurcations of periodic responses in nonlinear structures. ASME J Comput Nonlinear Dyn 8:021013 Formica G, Arena A, Lacarbonara W, Dankowicz H (2013) Coupling FEM with parameter continuation for analysis and bifurcations of periodic responses in nonlinear structures. ASME J Comput Nonlinear Dyn 8:021013
14.
Zurück zum Zitat Lenci S, Rega G (2015) Nonlinear free vibrations of planar elastic beams: a unified treatment of geometrical and mechanical effects, IUTAM Procedia (in press) Lenci S, Rega G (2015) Nonlinear free vibrations of planar elastic beams: a unified treatment of geometrical and mechanical effects, IUTAM Procedia (in press)
15.
Zurück zum Zitat Nayfeh A (2004) Introduction to perturbation techniques. Wiley-VCH, Weinheim. ISBN: 0-978-471-31013-6MATH Nayfeh A (2004) Introduction to perturbation techniques. Wiley-VCH, Weinheim. ISBN: 0-978-471-31013-6MATH
16.
Zurück zum Zitat Kovacic I, Rand R (2013) About a class of nonlinear oscillators with amplitude-independent frequency. Nonlinear Dyn 74:455–465MathSciNetMATH Kovacic I, Rand R (2013) About a class of nonlinear oscillators with amplitude-independent frequency. Nonlinear Dyn 74:455–465MathSciNetMATH
17.
Zurück zum Zitat Timoshenko S (1955) Vibrations problems in engineering. Wolfenden Press, New York. ISBN: 1406774650 Timoshenko S (1955) Vibrations problems in engineering. Wolfenden Press, New York. ISBN: 1406774650
18.
Zurück zum Zitat Huang TC (1961) The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions. ASME J Appl Mech 28:579–584MathSciNetMATH Huang TC (1961) The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions. ASME J Appl Mech 28:579–584MathSciNetMATH
19.
Zurück zum Zitat Lenci S, Rega G (2015) Asymptotic analysis of axial-transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions (submitted) Lenci S, Rega G (2015) Asymptotic analysis of axial-transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions (submitted)
20.
21.
Zurück zum Zitat Srinil N, Rega G (2007) The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables. Int J Non-Linear Mech 42:180–195MATH Srinil N, Rega G (2007) The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables. Int J Non-Linear Mech 42:180–195MATH
22.
Zurück zum Zitat Lagomarsino S, Penna A, Galasco A, Cattari S (2013) TREMURI program: an equivalent frame model for the nonlinear seismic analysis of masonry buildings. Eng Struct 56:1787–1799 Lagomarsino S, Penna A, Galasco A, Cattari S (2013) TREMURI program: an equivalent frame model for the nonlinear seismic analysis of masonry buildings. Eng Struct 56:1787–1799
Metadaten
Titel
A comprehensive analysis of hardening/softening behaviour of shearable planar beams with whatever axial boundary constraint
verfasst von
S. Lenci
F. Clementi
G. Rega
Publikationsdatum
08.02.2016
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 11/2016
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-016-0374-6

Weitere Artikel der Ausgabe 11/2016

Meccanica 11/2016 Zur Ausgabe

Nonlinear Dynamics, Identification and Monitoring of Structures

Hard loss of stability of Ziegler’s column with nonlinear damping

Nonlinear Dynamics, Identification and Monitoring of Structures

Dynamics of masonry walls connected by a vibrating cable in a historic structure

    Marktübersichten

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