两对边简支中间有任意多个单向弹性线支矩形板横向振动的一个解析解法*
An Analytical Solution of Transverse Vibration of Rectangular Plates Simply Supported at Two opposite Edges with Arbitrary Number of Elastic Line Supports in one Way
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摘要: 本文给出了两对边简支另两对边任意支承的中间有任意多个单向弹性线支矩形板横向振动的一个新的解析解法、将弹性线支反力看作是作用于板上的待求外力,求得了含有来知的弹性线支反力的两对边简支矩形板的运动方程的解析解;利用弹性线支反力与板横向位移之间的线性关系导出频率方程;频率方程及振型函数的表述均与已有方法不同.Abstract: This paper presents presents a new analytical solution of transverse vibration of rectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way.The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate.The analytical solution of the differential equation of motion of the rectangular plate,which includes the unknown reaction forces.is gained.The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and the transverse displacements of the plale along the elastic line supports.There presentations of foe frequency equation and the mode shape functions are different from those obtained by other methods.
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Key words:
- rectangular plate /
- eigen-frequency /
- elastic line support /
- analyticalSolution
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[1] A.S.Veletsos and N.M.Newmark,Determination of natural frequencies of continuous plates hinged along two opposite edges,Journal of Applied Mechanics,23(1956). [2] S.Azimi,J.F.Hamilton and W.Soedel,The receptance method applied to the free vibration of continuous rectangular plates,Journal of Sound and Vibration,93(1984). [3] M.Mukhopadhyay,A semi-anayltic solution for free vibration of rectangular plates,Journal of Sound and Vibration,60(1978). [4] E.E.Ungar,Free oscillations of edge-connected simply supported plate system,Journal of Engineering jor Industry,83(1961). [5] Y.K.Cheung and M.S.Cheung,Flexural vibrations of rectangular and other polygonal plates,Journal of the Engineering Mechanics Division,ASCE,97(1971). [6] 任永泰、史希福,《常微分方程》,辽宁人民出版社(1984). [7] 清华大学工程力学系振动组编,《机械振动(上册)》,机械工业出版社(1980). -
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