期刊
ENGINEERING STRUCTURES
卷 198, 期 -, 页码 -出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.engstruct.2019.109501
关键词
Piezoelectric cantilever plate; Nonlinear vibrations; Transverse and in-plane excitations; Resonant response; Chaotic motion
资金
- National Natural Science Foundation of China (NNSFC) [11832002, 11290152, 11427801]
- Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)
In this paper, the nonlinear vibrations of the laminated composite piezoelectric cantilever plate subjected to the transverse and in-plane excitations are investigated. Based on the Reddy's third-order plate theory and von Karman nonlinear strain-displacement relation, the nonlinear partial differential governing equations of motion are established for the laminated composite piezoelectric cantilever plate under combined the transverse and inplane excitations by applying Hamilton's principle. Employing Galerkin's approach, we discretize the continuous nonlinear dynamic equations of motion into the ordinary differential equations with four modes. Substituting the actual geometric and physical parameters of the laminated composite piezoelectric cantilever plate into the governing equation of motion, we use numerical method to investigate the effects of the lay-up parameters and the geometric parameters on the dimensionless natural frequencies of the cantilever plate. The amplitude-frequency response curves and the basin boundary diagram of two coexisting steady-state solutions are plotted for the laminated composite piezoelectric cantilever plate. The nonlinear dynamic responses of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations are investigated by changing the lay-up parameters, the transverse excitation, the voltage excitation and the in-plane excitation. The periodic, the quasi-periodic, the chaotic motions and the nonlinear stiffness characteristics can be found. The nonlinear dynamic behaviors help us to optimize the structural and physical parameters of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations.
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