Exact wave propagation analysis of moderately thick Levy-type plate with piezoelectric layers using spectral element method

Abstract

Spectral element method (SEM) is an accurate and efficient frequency domain-based method which has been frequently used in different analyses of various structures. In the present research, for the first time, this method is employed to deal with the wave propagation analysis of moderately thick rectangular plates with two piezoelectric layers attached on the top and bottom surfaces. The equations of motion are derived by taking into account the Mindlin plate theory assumptions and using the Hamilton's principle. The Maxwell's equation is employed to obtain the governing equation of electric potential in the piezoelectric layers. The differential equations are transformed into the frequency domain by employing the discrete Fourier transform and then a closed-form solution for the Levy type plate attached to piezoelectric layers is introduced. The dynamic stiffness matrix for the smart plate is obtained by applying the exact dynamic shape functions. Accurate and efficient numerical algorithms are introduced to extract the natural frequencies and the dynamic response of the structure under impact loading. The validation of the presented method is accomplished by comparing the obtained natural frequencies and dynamic response with the existing results in the literature and also the results obtained by the Abaqus software. Also, the effects of boundary condition and thickness of the plate and piezoelectric layers on the results are investigated. Independence to the mesh structure and less computational time are the most important advantages of the SEM compared with similar numerical methods like the finite element method.