Nonlinear vibrations of a composite circular plate with a rigid body

doi:10.1007/s10483-023-3005-8

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (6): 857-876.doi: https://doi.org/10.1007/s10483-023-3005-8

• 论文 • 下一篇

Nonlinear vibrations of a composite circular plate with a rigid body

Ying MENG, Xiaoye MAO, Hu DING, Liqun CHEN

Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China

收稿日期:2023-02-08 修回日期:2023-04-18 出版日期:2023-06-01 发布日期:2023-05-29
通讯作者: Liqun CHEN, E-mail: lqchen@shu.edu.cn
基金资助:
the National Natural Science Foundation of China (No. 12002195), the National Science Fund for Distinguished Young Scholars of China (No. 12025204), and the Program of Shanghai Municipal Education Commission of China (No. 2019-01-07-00-09-E00018)

Nonlinear vibrations of a composite circular plate with a rigid body

Ying MENG, Xiaoye MAO, Hu DING, Liqun CHEN

Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China

Received:2023-02-08 Revised:2023-04-18 Online:2023-06-01 Published:2023-05-29
Contact: Liqun CHEN, E-mail: lqchen@shu.edu.cn
Supported by:
the National Natural Science Foundation of China (No. 12002195), the National Science Fund for Distinguished Young Scholars of China (No. 12025204), and the Program of Shanghai Municipal Education Commission of China (No. 2019-01-07-00-09-E00018)

摘要/Abstract

摘要： The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical.

关键词: composite circular plate, weight, nonlinear vibration, equilibrium configuration, natural frequency

Abstract: The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical.

Key words: composite circular plate, weight, nonlinear vibration, equilibrium configuration, natural frequency

中图分类号:

74H45
74K20

Ying MENG, Xiaoye MAO, Hu DING, Liqun CHEN. Nonlinear vibrations of a composite circular plate with a rigid body[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 857-876.

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Nonlinear vibrations of a composite circular plate with a rigid body

Nonlinear vibrations of a composite circular plate with a rigid body

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