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

Abstract

<h2>Ruili SHEN Professor Southwest Jiaotong</h2><p>University, Chengdu, China</p><p>rlshen@163.com</p><p>Ruili Shen, born 1963, received his doctor’s degree from Southwest Jiaotong University, China. His main area of research is related to modern bridge design theory and bridge structural dynamics.</p><h2>Tao WANG</h2><p>Ph.D., Lecturer Southwest University of Science and Technology, Mianyang, China 7015294@qq.com</p><p>Tao Wang, born 1983, received his civil doctor’s degree from Southwest Jiaotong University, China. His main area of research is related to bridge structural dynamics.</p><p>In order to solve dynamic analysis of beams with variable cross-section more efficiently, taking a class of widely used beams as the breakthrough point, the calculation method was established based on the transfer matrix method. Firstly, taking a single-span beam as the basic element, the element transfer matrix of continuous beams with variable cross-section was derived by solving the partial differential equation of motion. Secondly, the boundary and continuity conditions at the supports were utilized to reduce the overall transfer matrix. Thirdly, the general algorithm for solving dynamic characteristics of continuous beams with variable cross-section was established to obtain the natural frequencies and the mode shapes. Finally, by employing New mark Beta Methods, dynamic analysis under moving loads was realized. And then, taking MATLAB as the platform, a numerical calculation program was developed to solve dynamic characteristics and dynamic analysis of beams with variable cross-section. The results show that, compared with the finite element method, the proposed method was verified to be accurate, simple, and efficient.</p>