两端固定超临界轴向运动梁横向平衡位形与振动  

Transverse equilibrium and vibration of axially moving beams with fixed boundaries in the supercritical regime

作　　者：张国策[1] 丁虎[1] 陈立群[1,2] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]上海大学力学系,上海200444

出　　处：《振动工程学报》2011年第1期8-13,共6页Journal of Vibration Engineering

基　　金：国家自然科学基金项目(10902064);国家杰出青年科学基金项目(10725209);上海市优秀学科带头人计划项目(09XD1401700);上海市重点学科建设项目(S30106);长江学者和创新团队发展计划基金课题(IRT0844)资助

摘　　要：研究了超临界速度下,两端固定的轴向运动梁静平衡位形及其分岔,以及横向非线性振动前两阶的固有频率。在超临界范围,轴向运动梁的静平衡位形由直线和对称曲线组成。基于轴向运动梁横向振动的非线性积分-偏微分控制方程,给出了固定边界条件下非平凡静平衡位形的解析表达式,讨论了梁的物理参数对轴向运动临界速度的影响。对于非平凡静平衡位形,经坐标变换,建立超临界轴向运动梁连续陀螺系统的标准控制方程。结合有限差分法以及离散傅立叶变换研究了超临界状态下梁横向振动的前两阶固有频率。并将数值结果与局部线性化后的Galerkin截断结果相比较。The equilibria,the bifurcation,and the first two supercritical natural frequencies of nonlinear transverse free vibrations of axially moving beams with fixed boundaries are investigated.In the supercritical transport speed ranges,the pattern of equilibria consists of the straight configuration and non-trivial solutions that bifurcate with transport speed.The equilibrium solutions are performed analytically for an axially moving beam with the fixed ends.The analysis results illustrate the tendencies of the critical speeds with the changing physical parameters.For motion about each non-trivial equilibrium configuration,the nonlinear integro-partial-differential equation is cast in the standard form of continuous gyroscopic systems by introducing a coordinate transform in the supercritical regime.Numerical schemes are presented for the governing equation via the finite difference method and the discrete Fourier transform for the natural frequencies of transverse vibrations.Numerical results indicate that the first natural frequencies of axially moving beams increase with the growth of axial speed.And the calculation results are confirmed qualitatively via the Galerkin method to truncate the corresponding governing equations without nonlinear parts.

关 键 词：轴向运动梁 非线性 静平衡位形 固有频率 超临界 

分 类 号：O32[理学—一般力学与力学基础]