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Nonlinear Vibration Analysis of Timoshenko Beams Using the Differential Quadrature Method

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Abstract

This paper addresses the large-amplitude free vibration of simplysupported Timoshenko beams with immovable ends. Various nonlineareffects are taken into account in the present formulation and thegoverning differential equations are established based on theHamilton Principle. The differential quadrature method (DQM) isemployed to solve the nonlinear differential equations. Theeffects of nonlinear terms on the frequency of the Timoshenkobeams are discussed in detail. Comparison is made with otheravailable results of the Bernoulli–Euler beams and Timoshenkobeams. It is concluded that the nonlinear term of the axial forceis the dominant factor in the nonlinear vibration of Timoshenkobeams and the nonlinear shear deformation term cannot be neglectedfor short beams, especially for large-amplitude vibrations.

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Authors and Affiliations

  1. Department of Civil Engineering, Tsinghua University, Beijing, 100084, P. R. China

    Hongzhi Zhong & Qiang Guo

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  1. Hongzhi Zhong
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  2. Qiang Guo
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Zhong, H., Guo, Q. Nonlinear Vibration Analysis of Timoshenko Beams Using the Differential Quadrature Method. Nonlinear Dynamics 32, 223–234 (2003). https://doi.org/10.1023/A:1024463711325

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