NUMERICAL VERIFICATION OF CALCULATION ON THE TRANSMISSION AND REFLECTION MATRIX OF BEAM WITH GRADUAL CHANGE CROSS-SECTION

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (3) : 274-280.

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NUMERICAL VERIFICATION OF CALCULATION ON THE TRANSMISSION AND REFLECTION MATRIX OF BEAM WITH GRADUAL CHANGE CROSS-SECTION

Lin Yaoxiong1, 2

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Abstract

Wave differential equation of prestressed box beam which has random cross-section was deduced. For the purpose of operating transmission and reflection coefficient matrix within segment with gradual change cross section on the prestressed beam, the segment was divided into several pieces of constant section beam. Transmission and reflection coefficient matrix of the amplitudes about the big end and the little end on the segment with non-uniform cross-section was operated based on the transfer matrix method from wave analysis on sandwich structure, and the matrix accuracy which was affected by the division number and cross-section dimension in the beam segment was analyzed by performing several subroutines programmed based on Maple software. The accuracy of method employed to operate transmission and reflection coefficient matrix within segment with gradual change cross section was verified using the solution of the wave differential equation according to the Galerkin method, combination of the first kind Bessel function was employed as trial function in the Galerkin method which was applied to solve the dynamic differential equation of the beam with gradual change cross-section. What is worth to be mentioned is that the trial function used in this paper can be used generally and more accurately to obtain the approximate solutions of differential equation of higher order which contained coefficients of series functions with the higher-order terms.

Key words

Beam with gradual change cross section / transmission and reflection coefficient matrix / the Galerkin method / elastic wave / the Bessel function combination

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Lin Yaoxiong;. NUMERICAL VERIFICATION OF CALCULATION ON THE TRANSMISSION AND REFLECTION MATRIX OF BEAM WITH GRADUAL CHANGE CROSS-SECTION[J]. Journal of Vibration and Shock, 2011, 30(3): 274-280