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2013 | OriginalPaper | Chapter

Viscous Damping, Plasticity and Buckling on Large Amplitude Vibrations of Beams

Author : Pedro Ribeiro

Published in: IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

Publisher: Springer Netherlands

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Abstract

Curious dynamic behaviour that beams may experience is discussed in this article. In the model of the beams a simple type of viscous damping, an elasto-plastic stress–strain relation and Von Kármán type of non-linearity are assumed. The continuum system is discretized following a finite element, p-version approach, and the equations of motion are numerically solved in the time domain. The analyses focuses on the qualitative differences that appear in the oscillations of damped beams when plasticity is present and on a buckling like phenomenon that plasticity may induce, leading to a dynamic behaviour difficult to anticipate.

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Literature
go back to reference Kaneko, T.: On Timoshenko’s correction for shear in vibrating beams. J. Phys. D 8, 1927–1936 (1975)CrossRef Kaneko, T.: On Timoshenko’s correction for shear in vibrating beams. J. Phys. D 8, 1927–1936 (1975)CrossRef
go back to reference Kojić, M., Bathe, K.-J.: Inelastic Analysis of Solids and Structures. Springer, Berlin (2005)MATH Kojić, M., Bathe, K.-J.: Inelastic Analysis of Solids and Structures. Springer, Berlin (2005)MATH
go back to reference Lee, J.-Y., Symonds, P.S., Borino, G.: Chaotic responses of a two-degree-of freedom elastic–plastic beam model to short pulse loading. Trans. ASME J. Appl. Mech. 59, 711–721 (1992)CrossRef Lee, J.-Y., Symonds, P.S., Borino, G.: Chaotic responses of a two-degree-of freedom elastic–plastic beam model to short pulse loading. Trans. ASME J. Appl. Mech. 59, 711–721 (1992)CrossRef
go back to reference Ma, G.W., Liu, Y.M., Zhao, J., Li, Q.M.: Dynamic asymmetrical instability of elastic–plastic beams. Int. J. Mech. Sci. 47, 43–62 (2005)MATHCrossRef Ma, G.W., Liu, Y.M., Zhao, J., Li, Q.M.: Dynamic asymmetrical instability of elastic–plastic beams. Int. J. Mech. Sci. 47, 43–62 (2005)MATHCrossRef
go back to reference Meirovitch, L.: Elements of Vibration Analysis, 2nd edn. McGraw-Hill, New York (1986) Meirovitch, L.: Elements of Vibration Analysis, 2nd edn. McGraw-Hill, New York (1986)
go back to reference Petyt, M.: Introduction to Finite Element Vibration Analysis. Cambridge University Press, Cambridge (1990)CrossRef Petyt, M.: Introduction to Finite Element Vibration Analysis. Cambridge University Press, Cambridge (1990)CrossRef
go back to reference Ribeiro, P.: A p-version, first order shear deformation, finite element for geometrically non-linear vibration of curved beams. Int. J. Numer. Method. Eng. 61, 2696–2715 (2004)MATHCrossRef Ribeiro, P.: A p-version, first order shear deformation, finite element for geometrically non-linear vibration of curved beams. Int. J. Numer. Method. Eng. 61, 2696–2715 (2004)MATHCrossRef
go back to reference Ribeiro, P.: On the predictability of elasto-plastic and geometrically non-linear oscillations of beams under harmonic excitation. Nonlinear Dyn. (2011). doi:10.1007/s11071-011-0104-5 Ribeiro, P.: On the predictability of elasto-plastic and geometrically non-linear oscillations of beams under harmonic excitation. Nonlinear Dyn. (2011). doi:10.​1007/​s11071-011-0104-5
go back to reference Ribeiro, P., van der Heijden, G.H.M.: Elasto-plastic and geometrically nonlinear vibrations of beams by the p-version finite element method. J. Sound Vib. 325, 321–337 (2009)CrossRef Ribeiro, P., van der Heijden, G.H.M.: Elasto-plastic and geometrically nonlinear vibrations of beams by the p-version finite element method. J. Sound Vib. 325, 321–337 (2009)CrossRef
go back to reference Symonds, P.S., Yu, T.X.: Counter-intuitive behavior in a problem of elastic–plastic beam dynamics. Trans. ASME J. Appl. Mech. 52, 517–522 (1985)CrossRef Symonds, P.S., Yu, T.X.: Counter-intuitive behavior in a problem of elastic–plastic beam dynamics. Trans. ASME J. Appl. Mech. 52, 517–522 (1985)CrossRef
go back to reference Woinowski-Krieger, S.: The effect of an axial force on the vibration of hinged bars. J. Appl. Mech. 17, 35–36 (1950)MathSciNet Woinowski-Krieger, S.: The effect of an axial force on the vibration of hinged bars. J. Appl. Mech. 17, 35–36 (1950)MathSciNet
Metadata
Title
Viscous Damping, Plasticity and Buckling on Large Amplitude Vibrations of Beams
Author
Pedro Ribeiro
Copyright Year
2013
Publisher
Springer Netherlands
DOI
https://doi.org/10.1007/978-94-007-5742-4_8

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