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.
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Conflict of interest Liqun CHEN and Hu DING are editorial board members for Applied Mathematics and Mechanics (English Edition) and were not involved in the editorial review or the decision to publish this article. The authors declare no conflict of interest.
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Project 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)
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Meng, Y., Mao, X., Ding, H. et al. Nonlinear vibrations of a composite circular plate with a rigid body. Appl. Math. Mech.-Engl. Ed. 44, 857–876 (2023). https://doi.org/10.1007/s10483-023-3005-8
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DOI: https://doi.org/10.1007/s10483-023-3005-8