Yin Xiaochun. Simplification of Frequency Equation of Multilayered Cylinders and Some Recursion Formulae of Bessel Functions[J]. Applied Mathematics and Mechanics, 1999, 20(3): 319-324.
 Citation: Yin Xiaochun. Simplification of Frequency Equation of Multilayered Cylinders and Some Recursion Formulae of Bessel Functions[J]. Applied Mathematics and Mechanics, 1999, 20(3): 319-324.

# Simplification of Frequency Equation of Multilayered Cylinders and Some Recursion Formulae of Bessel Functions

• Rev Recd Date: 1999-01-09
• Publish Date: 1999-03-15
• 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.
•  [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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