摘要
针对有限元法等数值方法较难处理的质量偏心梁问题,考虑质心、形心不重合情形下的弯-纵耦合效应,建立了有偏心Timoshenko梁弯-纵耦合振动的数学模型,推导了相应的特征方程。进而给出了若干偏心工况下Timoshenko梁弯-纵耦合振动的解析表达式,并探讨了偏心率和典型边界条件对纵向和弯曲振动固有频率和模态振型的影响规律。分析结果表明,固有频率随着偏心率的增大而减小,且质量偏心对纵向振动的影响较弯曲振动更为明显。
Natural vibration of a beam with mass eccentricity is difficult to deal with using numerical methods,such as,the finite element method. Considering the coupling effect caused by the center of mass not coinciding with the center of geometry,the mathematical model of a Timoshenko beam＇s flexural-longitudinal coupled vibration was established,the corresponding characteristic equation was derived. Then the analytic solutions to Timoshenko beam＇s flexural-longitudinal coupled natural vibration under several mass eccentric conditions were deduced. The effect laws of eccentricities and boundary conditions on the natural frequencies and modal shapes of flexural-longitudinal coupled natural vibration were explored. The results showed that the natural frequencies decrease with increase in eccentricity,and the effects of eccentricity on the longitudinal vibration are more obvious than those on the flexural vibration.
出处
《振动与冲击》
EI
CSCD
北大核心
2015年第19期8-12,36,共6页
Journal of Vibration and Shock
基金
国家自然科学基金项目(11172166)
