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Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections

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Abstract

This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.

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Authors and Affiliations

  1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510640, China

    Zhaoting Chen, Ronghui Wang, Li Chen & Chunguang Dong

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  1. Zhaoting Chen
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  2. Ronghui Wang
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  3. Li Chen
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  4. Chunguang Dong
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Correspondence to Zhaoting Chen.

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Recommended by Associate Editor Ohseop Song

Zhaoting Chen is a doctoral candidate pursuing a Ph.D. degree in Bridge and Tunnel Engineering at South China University of Technology, China. His current research area is mainly on the nonlinear dynamics analysis of stiffened plate using analytical method.

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Chen, Z., Wang, R., Chen, L. et al. Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. J Mech Sci Technol 30, 3469–3476 (2016). https://doi.org/10.1007/s12206-016-0706-4

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  • DOI: https://doi.org/10.1007/s12206-016-0706-4

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