A weak form quadrature element method for nonlinear free vibrations of Timoshenko beams
Abstract
Purpose
The purpose of this paper is to highlight the implementation of a recently developed weak form quadrature element method for nonlinear free vibrations of Timoshenko beams subjected to three different boundary conditions.
Design/methodology/approach
The design of the paper is based on considering the geometrically nonlinear effects of axial strain, bending curvature, and shear strain. Then the quadrature element formulation of the beam is introduced.
Findings
The efficiency of the method is demonstrated by a convergence study. Ratios of the nonlinear fundamental frequencies to the corresponding linear frequencies are extracted. Their variations with the ratio of amplitude to radius of gyration and the slenderness ratio are examined. The effects of the nonlinearity on higher order frequencies and mode shapes are also investigated.
Originality/value
The computed results show fast convergence and compare well with available literature results.
Keywords
Acknowledgements
The present study was supported by the National Natural Science Foundation of China (Grant No. 11402040), the Fundamental Research Funds for the Central Universities of China (Grant Nos CDJZR12205529 and CDJZR14205550), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130191120047), and the Frontier and Application Basic Research Program of Chongqing Science and Technology Commission (Grant No. cstc2014jcyjA30002).
Citation
Liao, M. and Zhong, H. (2016), "A weak form quadrature element method for nonlinear free vibrations of Timoshenko beams", Engineering Computations, Vol. 33 No. 1, pp. 274-287. https://doi.org/10.1108/EC-09-2014-0183
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited