Applied Mathematics and Mechanics >
Nonlinear free vibration of piezoelectric cylindrical nanoshells
Received date: 2018-09-12
Revised date: 2018-10-30
Online published: 2019-05-01
Supported by
Project supported by the National Natural Science Foundation of China (No. 11672071) and the Fundamental Research Funds for the Central Universities (No. N170504023)
The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then, the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.
Yanqing WANG, Yunfei LIU, J. W. ZU . Nonlinear free vibration of piezoelectric cylindrical nanoshells[J]. Applied Mathematics and Mechanics, 2019 , 40(5) : 601 -620 . DOI: 10.1007/s10483-019-2476-6
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