등변분포 평면응력을 받는 SS-C-SS-C 직사각형 판의 진동과 좌굴의 엄밀해

초록

Exact solutions are presented for the free vibration and buckling of rectangular plates having two opposite edges (=0 and a) simply supported and the other two (=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress , where h is the plate thickness. By assuming the transverse displacement () to vary as , the governing partial differential equation of motion is reduced to an ordinary differential equation in with variable coefficients, for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at =0 and byields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters =0, 0.5, 1, 1.5, 2, for which =2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for =0, 1, 2 obtained by the method of integration of the differential equation (=0) or the method of energy (=1, 2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios =0.5, 1, 2 when =2, with load intensities =0, 0.5, 0.8, 0.95, 1, where is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes are also shown.

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