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Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

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Abstract

In this study, a unified nonlinear dynamic buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear dynamic buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for dynamic buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the dynamic buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural dynamic buckling behavior in the presence of damping effects under thermal environment are conducted.

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Acknowledgements

The work presented in this paper was supported by Australian Research Council Projects DP160103919 and DP140101887.

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  1. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Kang Gao, Wei Gao, Di Wu & Chongmin Song

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  1. Kang Gao
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Correspondence to Wei Gao.

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Gao, K., Gao, W., Wu, D. et al. Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment. Nonlinear Dyn 90, 2423–2444 (2017). https://doi.org/10.1007/s11071-017-3811-8

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