变截面梁动力响应的频域传递矩阵计算方法  

The Calculating Method of Dynamic Analysis of Beam with Variable Cross-Section Based on the Frequency-Domain Transfer Matrix Method

作　　者：王渊[1] 沈锐利[1] 王路[1] WANG Yuan;SHEN Ruili;WANG Lu(School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China)

机构地区：[1]西南交通大学土木工程学院,四川成都610031

出　　处：《力学季刊》2018年第1期191-200,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(51178396)

摘　　要：为提高变截面梁振动分析的计算效率,提出了基于频域传递矩阵法的动力计算算法.首先,选择线速度、角速度、弯矩和剪力作为求解变量,通过Laplace变换将变截面梁的动力响应时域偏微分方程转换为频域常微分方程;然后,通过求解频域方程并结合协调和边界条件建立变截面梁的频域传递矩阵;通过构造傅里叶级数展开形式的时域响应函数,对变截面梁传递矩阵方法求解的频响函数进行Laplace逆变换,建立了变截面梁的固有特性计算和时域瞬态响应计算方法,最后,借助数值仿真软件,开发了变截面梁动力响应分析的计算程序.完成对算例的仿真计算和分析,并与有限元计算结果进行对比,数值结果验证了该方法的正确性和有效性.In order to solve the dynamic responses of beams with varying cross-section more efficiently, a calculation method was established based on the frequency-domain transfer matrix method. Firstly, linear velocity, angular velocity, bending moment and shear force were taken as analyzing variables. Using Laplace transformation, the time-domain partial differential equations of beams with varying cross-section were transformed to the ordinary differential equations in frequency-domain. Secondly, employing the compatibility and boundary conditions and solving the equations in frequency domain, an analytical solution for the beam element was obtained, and then the element transfer matrix of beams with varying cross-section was derived. Thirdly, constructing time-domain response functions by Fourier series expansion and applying the numerical inversion of Laplace transform to the transfer matrix, the transient response of beams with varying cross-section in time-domain was obtained. Finally, utilizing MATLAB for programming, the inherent characteristic analysis and the dynamic analysis for beams with varying cross-section were accomplished. Compared with the finite element method, the proposed calculation methods are validated to be correct and effective.

关 键 词：频域传递矩阵法 LAPLACE逆变换 变截面梁 固有特性分析 动力时程分析 

分 类 号：TU317[建筑科学—结构工程]