非保守力作用下简支梁在屈曲附近的自由振动  

FREE VIBRATION OF A SIMPLY SUPPORTED BEAM UNDER A NON-CONSERVATIVE DISTRIBUTED LOAD

作　　者：李清禄[1] 杨静宁[1] 

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《力学与实践》2014年第3期333-336,340,共5页Mechanics in Engineering

基　　金：国家自然科学基金(11272278;11262010);甘肃省自然科学基金(2011GS04154)资助项目

摘　　要：对受非保守载荷的简支梁在后屈曲附近的自由振动进行了研究.基于可伸长梁的大变形理论,建立了受沿轴线分布切向非保守力作用的简支梁后屈曲附近自由振动的几何非线性模型.在小振幅和谐振动假设下,简化得到后屈曲梁线性振动的控制方程.采用打靶法求解振动问题的控制方程,给出了前三阶固有频率与载荷之间的特征关系曲线.结果表明:非保守载荷作用下梁的振动响应与保守载荷作用下梁的振动响应有着明显不同.The free vibration of post-buckling beams subjected to non-conservative load is studied. Based on the large deformation theory for the elastic beams, the geometrically nonlinear dynamic equations are established for beams subjected to a distributed tangential follower force along the central axis. By assuming that the amplitude of beam＇s vibration is small and its response harmonic, a linear version of the vibration problem is deduced. By employing the numerical shooting technique to solve the governing equations for vibration, numerical solutions of the first three natural frequencies against the load parameter are obtained. The results show that the features of the vibration response of the beams subjected to a non-conservative load are evidently different from those subjected to a conservative load.

关 键 词：简支梁 非保守力 自由振动 固有频率 打靶法 

分 类 号：O343[理学—固体力学]