复模态分析超临界轴向运动梁横向非线性振动

摘要

近似解析研究了简支边界条件下超临界轴向运动梁横向非线性自由振动的固有频率和模态函数。采用复模态方法处理控制方程，一个积分偏微分方程。将 Galerkin 截断思想用于近似处理线性化方程，一个含空间依赖系数的常微分方程。给出了不同截断项数对固有频率的影响。基于8项截断，讨论了系统参数对模态函数的影响。%Under the simply supported boundary conditions,the natural frequencies and modal functions of transversally nonlinear free vibrations of axially moving beams were approximately analyzed in the supercritical re-gime.Complex modal analysis method was devoted to the governing equation,an integro-partial-differential equa-tion.Galerkin method was applied for the linear standard equation,an ordinary differential equation with a spa-tially dependent coefficient.The effects of different truncations on natural frequencies were shown.Based on the 8-term Galerkin truncation,the effects of system parameters on modal functions were discussed.