스펙트럴 요소법을 이용한 동적집중하중을 받는 평판의 진동해석

초록

A spectral element method(SEM) is introduced for the vibration analysis of the rectangular plates subject to dynamic concentrated loads. First the spectral plate element is derived from the relations between the forces and displacements along the two opposite edges of plate elements. The global spectral matrix equation is then formulated by assembling two spectral plate elements so that the dynamic concentrated load is located at the connection nodal line between two plate elements. The concentrated load is then spatially Fourier transformed in the direction of the connection nodal line to transform the two-dimensional plate problem into a simplified equivalent one-dimensional beam-like problem. We may benefit from these procedures in that the spectral analysis method developed for beam in the previous study can be readily applied. The numerical results from the present SEM is compared with the exact analytical solutions to prove the remarkable accuracy of the present SEM is compared with the exact analytical solutions to prove the remarkable accuracy of the present SEM, while this is not true for the conventional finite element solutions, especially at high frequency.