Solutions of nonlinear thickness-shear vibrations of an infinite isotropic plate with the homotopy analysis method |
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Authors: | Rongxing?Wu Email author" target="_blank">Ji?WangEmail author Jianke?Du Yuantai?Hu Hongping?Hu |
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Institution: | 1.Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics,Ningbo University,Ningbo,China;2.Department of Mechanics, School of Civil Engineering and Mechanics,Huazhong University of Science and Technology,Wuhan,China |
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Abstract: | As a preliminary attempt for the study on nonlinear vibrations of a finite crystal plate, the thickness-shear mode of an infinite
and isotropic plate is investigated. By including nonlinear constitutive relations and strain components, we have established
nonlinear equations of thickness-shear vibrations. Through further assuming the mode shape of linear vibrations, we utilized
the standard Galerkin approximation to obtain a nonlinear ordinary differential equation depending only on time. We solved
this nonlinear equation and obtained its amplitude–frequency relation by the homotopy analysis method (HAM). The accuracy
of the present results is shown by comparison between our results and the perturbation method. Numerical results show that
the homotopy analysis solutions can be adjusted to improve the accuracy. These equations and results are useful in verifying
the available methods and improving our further solution strategy for the coupled nonlinear vibrations of finite piezoelectric
plates. |
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Keywords: | |
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