Exact frequency-domain spectral element model for the transverse vibration of a reangular Kirchhoff plate

As an extension of the previous work on membranes by Kim and Lee (2020), an exact frequency-domain spectral element model is proposed for the transverse vibrations of a rectangular Kirchhoff plate, based on the following procedure. First, in the frequency-domain, the general solution of a finite rectangular plate element is derived in the spectral form in the spatial domain, after removing all the trigonometric terms that vanish at the four boundary edges. Second, as an important theoretical improvement, the boundary functions that represent the boundary conditions at the four boundary edges are also expressed in the spectral forms in the spatial domain. Next, by using the projection method based on the orthogonality of trigonometric functions, the spatial-domain spectral coefficients of the general solution are related to those of the boundary functions. Finally, from the force-displacement relationships, the spectral element matrix (or dynamic stiffness matrix) is formulated for a finite rectangular plate element. As both the general solution and boundary functions are expressed in the spectral forms in both the temporal and spatial domains, a fast Fourier transform (FFT) algorithm can be applied to efficiently simulate the vibration responses and waves in a plate. The accuracy and computational efficiency of the proposed SEM are evaluated by comparison with the exact theory, modal analysis method, and the commercial finite-element-analysis software ANSYS. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents an exact frequency-domain spectral element model for the transverse vibrations of a rectangular Kirchhoff plate. The model utilizes spectral forms of the general solution and boundary functions to establish relationships between spatial-domain spectral coefficients through projection method, and formulates a spectral element matrix to simulate the vibration responses and wave propagation in the plate.