渐变截面梁波透射反射系数求解的数值验证

林耀雄;

振动与冲击 ›› 2011, Vol. 30 ›› Issue (3) : 274-280.

PDF(1238 KB)
PDF(1238 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (3) : 274-280.
论文

渐变截面梁波透射反射系数求解的数值验证

  • 林耀雄1, 2
作者信息 +

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

  • Lin Yaoxiong1, 2
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文章历史 +

摘要

推导任意截面形状的预应力Timoshenko梁波动微分方程,对预应力箱板梁渐变截面段弹性波透(反)射系数矩阵进行计算,为求得小端传播到大端的透射波幅值,将渐变截面梁近似当作具有一系列截面间断的阶梯梁,按层状结构波传播的传递矩阵法求波幅在大小端间的透(反)射系数矩阵,通过基于Maple软件平台编写子程序对梁截面尺寸及渐变段分段数目对透(反)射系数矩阵精确性的影响进行数值分析。在波动微分方程伽辽金近似解基础上,对渐变截面段梁波透(反)射系数矩阵的求解法进行数值验证,验证中以第一类贝塞尔函数组合作为系数具有高次项幂级数函数的高阶常微分方程伽辽金法近似解的试函数,该试函数对这类方程具有普遍的适用性。

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.

关键词

渐变截面梁 / 透(反)射系数矩阵 / 伽辽金法 / 弹性波 / 贝塞尔函数组合

Key words

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

引用本文

导出引用
林耀雄;. 渐变截面梁波透射反射系数求解的数值验证[J]. 振动与冲击, 2011, 30(3): 274-280
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

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