Simplification of Frequency Equation of Multilayered Cylinders and Some Recursion Formulae of Bessel Functions
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摘要: 本文从理论上研究了相同材料的多层厚壁圆筒径向振动的频率方程,证明若干层相互接触的层筒的整体频率方程,可以用单个厚壁圆筒的频率方程替代,从而大大简化了求解过程.并从该实际问题出发,推导出了一类贝塞尔函数的递推公式.Abstract: In this paper the axially symmetric, radial vibration frequency equation of multilayered cylinders made of the same materials in plain strain state is studied. It is proved in this paper that the frequency equation of several contact hollow cylinders can be replaced by the frequency equation of a single hollow cylinder,so that the solving process is greatly simplified. Some recursion formulae of Bessel functions are derived from such practice problems as well.
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Key words:
- frequency /
- vibration /
- Bessel functions
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[1] Wang X,Gong Y N.An elastodynamic solution for multilayered cylinders[J].Int J Engng Sci,1992,30(1):25～33 [2] Eringen A C,Sububi E S.Elastodynamics,Vol.2,Linear Theory[M].New York:Academic Press,1975 [3] Yin Xiaochun.Radial impact of two concentric elastic hollow cylinders[A].19th ICTAM[C],Abstract KS7-04,Kyoto:1996 [4] Gong Y N,Wang X.Radial Vibrations and dynamic stresses in elastic hollow cylinder[A],Structural Dynamics:Recent Advances[M].England:Elsevier Science Publication Ltd,1991,137～147 [5] Gazis D C.Exact analysis of the plain strain vibration of thick-wall hollow cylinders[J].The J Acoust Soc Amer,1958,30(5):786～794 -
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