边缘有弹性点支矩形板的横向振动<sup>*</sup>

边缘有弹性点支矩形板的横向振动^*

基金项目: * 华东工学院科研基金资助

摘要: 本文研究了两对边简支、另两对边任意支承的自由边有弹性点支的矩形板的横向振动问题,提供了一种求其固有频率和振型的高精度解法,自由边上弹性点支的个数及位置均可任意,本文用脉冲函数表示弹性点支的反力和力矩,利用Fourier级数将脉冲函数沿边缘展开,从而得到了满足全部边界条件的特征方程,可求得任意精度的任意阶固有频率及振型.

Abstract: This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points.The number and location of these points on free edges may be completely arbitrary.This paper uses impulse function to represent reaction and moment at points.Fourter series is used to expand the impulse function along the edges.Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.

[1]	Cox,H.L.and J.Boxer,Vibration of rectangular plates point-supported at corners,Aeronautical Quaricrly,11(1960).
[2]	Reed,R.E.,Comparison of methods in calculating frequencies of corner-supported rectangular plates,NASA TN D-3030(1965).
[3]	Kirk,C.L.,A note on the lowest natural frequency of square plate point-supported at the corners,J.the Royal Aeronautical Society,66(1962).
[4]	Kerstens,L.G.M.,Vibration of a rectangular plate supported at an arbitrary number of points,J.Sound and Vibration,65(1979).
[5]	Gorman,D.J.,Free vibration analysis of rectangular plates with symmetrically distributed point supports along the edges,J.Sound and Vibration,73(1980).
[6]	Gorman,D.J.,An analytical solution for the free vibration analysis of rectangular platess resting on symmetric point supports,J.Sound and Vibration,79(1981).
[7]	Gorman,D.J.,Vibration of Rectangular Plates,New York,Elsevier North Holland(1982).
[8]	Bapat,A.V.and N.Venkatramani,A new approach for the representation of a point support in the analysis of plates,J.Sound and Vibration,120(1988).
[9]	Bapat,A.V.and N.Venkatramani,Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates,J.Sound and Vibration,120(1988).