用积分方程法解板的振动问题<sup>*</sup>

许明田; 程德林

用积分方程法解板的振动问题^*

山东工业大学数理系济南 250014

基金项目: * 山东省自然科学基金

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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

Solving Vibration Problem of Thin Plates Using Integral Equation Method

Department of Mathematics and Physics, Shandong University of Technology, Jinan 250014, P. R. China

摘要

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。
- 积分方程 /
- 薄板 /
- 振动
Abstract: This paper deals with reducing differential equations of vibration problem of plates with concentrated masses, elastic supports and elastically mounted masses into eigenvalue problem of integral equations. By applying the general function theory and the integral equation theory. the frequency equation is derived in terms of standard eigenvalue problem of a matrix with infinite order. So that, the natural frequencies and mode shapes can be determined. Convergence of this method has also been, discussed at the end of this paper.
- integral equation /
- thin plate /
- vibration

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参考文献(11)

[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)