有限要素法による平板の固有振動数の誤差 : インバースパワ法の場合

概要

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This paper describes the accuracy of the natural frequency calculation by FEM (Finite Element Method) which is influenced by the number and shape of elements. For this purpose, natural frequencies of a square plate and a rectangular plate, both with four simply supported egdes, are calculated by FEM and compared with the analytical solutions. The shapes of elements selected are square, rectangle and right-angle triangle, and the plate is divided into uniform mesh of respective element. Natural frequencies are culculated by inverse power method. As the number of mesh increases, the results of the FEM calculation converge to the analytical value of the natural frequency of the plate. In case of the rectangular element, the accuracy of the calculation using the rectangular element with an aspect ratio of about 1/2 is better than the one using the square element. And in case of the triangular element, the accuracy of the calculation using the right-angle isoscales triangle is better than the one using other triangular element. Young's modulus (E) and Poisson's ration (ν) of the plate have little influence to the accuracy of the calculation.
東海大学の論文