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.

# Solving Vibration Problem of Thin Plates Using Integral Equation Method

• Rev Recd Date: 1996-03-25
• Publish Date: 1996-07-15
• 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.
•  [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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