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边缘有弹性点支矩形板的横向振动*

周叮

周叮. 边缘有弹性点支矩形板的横向振动*[J]. 应用数学和力学, 1989, 10(10): 929-938.
引用本文: 周叮. 边缘有弹性点支矩形板的横向振动*[J]. 应用数学和力学, 1989, 10(10): 929-938.
Zhou Ding. Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges[J]. Applied Mathematics and Mechanics, 1989, 10(10): 929-938.
Citation: Zhou Ding. Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges[J]. Applied Mathematics and Mechanics, 1989, 10(10): 929-938.

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

Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges

  • 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.
  • [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).
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出版历程
  • 收稿日期:  1988-08-04
  • 刊出日期:  1989-10-15

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