受弹性点支的任意形状的膜的振动

周叮

受弹性点支的任意形状的膜的振动

周叮

华东工学院

基金项目: 华东工学院科研发展基金资助

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出版历程
- 收稿日期: 1988-09-14
- 刊出日期: 1989-12-15

Vibration of Arbitrarily Shaped Membranes with Elastical Supports at Points

Zhou Ding

East China Institute of Technology, Nanjing

摘要

摘要: 本文提供了一个求解受弹性点支的任意形状的膜的振动的新方法.将弹性点支反力看作是作用于膜上的未知外力,求出了包含有未知反力的运动方程的精确解,利用弹性点支处位移和反力的线性关系导出频率方程.最后以受弹性点支的圆膜为例给出了其频率方程的具体计算公式,并数值计算了受两个对称弹性点支的圆膜的固有振动频率.

Abstract: This paper presents a new method for solving the vibration of arbitrarily shaped membranes with elastical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.

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参考文献(9)

[1]	Steele,C.W.,Numerical computation of electric and magnetic field in a uniform waveguide of arbitrary cross-section,Journal of Computational Physics,3(1968).
[2]	Bates,R.H.T.,The theory of point-matching method for perfectly conducting waveguides and transmission lines,Institution of Electrical and Electronic Engineers Transactions on Microwave Theory and Techniques,MTT-17(1969).
[3]	Bullcy,R.M.and J.B.Davies,Computation of approximate polynomial solutions to TE modes in an arbitrary shaped waveguide,Institution of Electrical and Electronic Engineers Transactions on Microwave Theory and Techniques,MTT-17(1969).
[4]	Laura,P.A.A.,A simple method for the caleulation of cut-off frequencies of waveguide with arbitrary cross-section,Proceedings of the Institution of Electrical and Electronic Engineers(1966),54.
[5]	Arlett,P.L.,A.K.,Bahrani and O.C.Zienkiewicz,Application of finite elements to the solution of Helmholtz's equation,Proceeding of the Institution of Electrical Engineers(1968),115.
[6]	Laura,P.A.A.,W.,Romanelli and M.J.Maurizi,On the analysis of waveguides of doublyconnected cross-section by the method of conformal mapping,Journal of Sound and Vibration,20(1972).
[7]	Mazumdar,J.,Transverse vibration of membranes of arbitrary shape by the method of constant-deflection contours,Journal of Sound and Vibration,27(1973).
[8]	Nagaya,K.,Vibrations and dynamic response of membranes with arbitrary shape,American Society of Mechanical Engineers Journal of Applied Mechanics,45(1978).
[9]	Nagaya,K.,Vibration of an arbitrarily shaped membrane with point supports,Journal of Sound and Vibration,65(1979).