Timoshenko薄壁梁双向弯曲与扭转耦合的振动方程及求解  

Solution of oscillation equation in timoshenko thin-walled beam considering coupled compound bending and twisting

作　　者：黄君毅 王勇[2] 罗旗帜[3] 

机构地区：[1]广州市鲁班建筑防水补强公司,广东广州510665 [2]华南理工大学交通与土木学院,广东广州510641 [3]佛山科学技术学院土木工程与建筑系,广东佛山528000

出　　处：《佛山科学技术学院学报（自然科学版）》2009年第1期54-58,66,共6页Journal of Foshan University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50378019);广东省自然科学基金资助(034066)

摘　　要：基于薄壁杆件理论,研究了Timoshenko薄壁梁双向弯曲与扭转耦合的振动问题。根据Timoshenko梁的受力特性,考虑了剪切效应影响,给出了薄壁梁质点的位移系数和空间位移场。根据能量泛函变分原理导出了Timoshenko薄壁梁的振动微分方程。运用降阶法和频率扫描法求得微分方程的解析解。算例计算表明,此解析解与有限元法的结果吻合较好。Based on the theory of thin-walled structures, the coupled bending and torsional vibration of thin-walled beam was researched in this paper. The displacement parameters and space displacement field of thin-walled beam were given by considering shearing effect and mechanic performance of timoshenko beam. Oscillatory differential equation of the timoshenko thin-walled beam was deduced based on functional variation principle. Analytic solution of differential equation was deduced by using method of order reducing and frequency sweep method. Calculation examples show that the results of this paper agree well with the results of finite element method.

关 键 词：Timoshenko薄壁梁 弯扭耦合 振动微分方程 解析解 

分 类 号：O326[理学—一般力学与力学基础]