粘弹性Winkler地基上Bernoulli-Euler梁横向自振特性  

Transverse Natural Vibration Characteristics of Bernoulli-Euler Beam on Viscoelastic Winkler Foundation

作　　者：付艳艳[1] 余云燕[1] FU Yan-yan;YU Yun-yan(School of Civil Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学土木工程学院,兰州730070

出　　处：《兰州交通大学学报》2020年第6期21-25,31,共6页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(51268031,11662007);甘肃省基础研究创新群体(145RJIA332)。

摘　　要：以粘弹性Winkler地基上Bernoulli-Euler梁为目标,研究其在经典边界条件下的横向自由振动特性.基于回传射线矩阵法,根据振动控制方程及边界耦合条件推导得到各经典边界条件下的频率方程,进而求解得到粘弹性Winkler地基上Bernoulli-Euler梁在两端简支边界条件下的自振频率的解析解、其他边界条件下自振频率的近似解析解及衰减系数的解析解;最后,在单一局部坐标系下推导了各经典边界条件下的模态函数表达式.为地基梁振动特性的研究提供理论基础.In this paper,the Bernoulli-Euler beam on viscoelastic Winkler foundation is studied for its transverse free vibration characteristics under classical boundary conditions.Based on the method of reverberation-ray matrix,the frequency equations under various boundary conditions are derived according to vibration equation and boundary coupling conditions.Then,the analytic solution of natural frequencies of Bernoulli-Euler beam on viscoelastic Winkler foundation under simply supported boundary condition,approximate analytic solutions of natural frequencies under other boundary conditions and analytic solutions of attenuation coefficients are obtained.Finally,the modal functions under each boundary condition are derived in a single local coordinate system,which provides a theoretical basis for the study of vibration characteristics of foundation beams.

关 键 词：粘弹性Winkler地基 Bernoulli-Euler梁 横向自由振动特性 回传射线矩阵法 

分 类 号：TU470[建筑科学—结构工程] O327[建筑科学—土工工程]