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用积分方程法解板的振动问题*

许明田 程德林

许明田, 程德林. 用积分方程法解板的振动问题*[J]. 应用数学和力学, 1996, 17(7): 655-660.
引用本文: 许明田, 程德林. 用积分方程法解板的振动问题*[J]. 应用数学和力学, 1996, 17(7): 655-660.
Xu Mingtian, Cheng Delin. Solving Vibration Problem of Thin Plates Using Integral Equation Method[J]. Applied Mathematics and Mechanics, 1996, 17(7): 655-660.
Citation: Xu Mingtian, Cheng Delin. Solving Vibration Problem of Thin Plates Using Integral Equation Method[J]. Applied Mathematics and Mechanics, 1996, 17(7): 655-660.

用积分方程法解板的振动问题*

基金项目: * 山东省自然科学基金

Solving Vibration Problem of Thin Plates Using Integral Equation Method

  • 摘要: 本文把带有集中质量、弹性支承和弹簧支撑着的质量块(振子)的薄板的振动微分方程化成为积分方程的特征值问题。然后利用广义函数理论和积分方程理论,得到了用一无穷阶矩阵的标准特征值形式给出的频率方程,从而方便地得到了固有频率和振型。并讨论了这种方法的收敛性。
  • [1] Xu Mingtian and Chen Delin,A new approach to solve a type of vibration problems,Journal of Sound and Vibration,177,4(1994),565-571.
    [2] Ming Unejen and E.B.Magrab,Natural frequencies and mode shapes of beams carrying a two degree-of-freedom spring-mass system,Transactions of the.9SME,Journal of Vihrariou and Acoustics,115(1993),202-209.
    [3] T.H.Christopher and M.A.Baker,The Numerical Treatment Integral Equations,Clarendon Press,Oxford(1967).
    [4] L.Ercoli and P.A.A.Laura,Analytical and experiment investigation on continuous beams carrying elastically mounted masses,Jorrrrral of Sound and Vibration,114(1987),519-533.
    [5] M.S.Ingber,A.L.Pate and J.M-Salazar,Vibration of a clamped plate with concen-trated mass and spring attachments,Jorrrual of Sound arrd Vibration,153(1992),142-166.
    [6] E.H.Dowcll,On some general properties of combined dynamical systems,ASME Journal of Applied Meclrarrics,46(1979),206-209.
    [7] J.W.Nicholson and L.A.I3ergman,Free vibration of combined dynamical systems,Journall of Engineering Mechanics,112(1986),1-13.
    [8] D.N.Manikanahally and M.J.Crocker,Vibration absorbers for hystcrctically damped mass-loaded beams,ASME Jourunall of Vibration Acoustics,113(1991),116-122.
    [9] C.S.Kim and S.M.Dickinson,On the analysis of laterally vibrating slender beams subject to various complicating effects,Journal of Soundl and Vinbration,122,3(1988).44l-455.
    [10] P.L.Vcmicre de Irassar,G.M.Ficcadenti and P.A.A.Laura,Dynamic analysis of a beam with an intermediate elastic support.Journal of Sound and Vibration.96,3(1984),381-389.
    [11] 严宗达,《结构力学中的富里叶级数解法》,天津大学出版社(1989)
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出版历程
  • 收稿日期:  1994-11-15
  • 修回日期:  1996-03-25
  • 刊出日期:  1996-07-15

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