超临界轴向运动梁横向非线性振动频域分析  

FREQUENCY DOMAIN ANALYSIS OF SUPERCRITICAL NONLINEAR VIBRATION OF AXIALLY MOVING BEAMS

作　　者：丁虎[1] 张国策[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：《固体力学学报》2011年第4期360-364,共5页Chinese Journal of Solid Mechanics

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);上海高校选拔培养优秀青年教师科研专项基金项目(B37-0101-08-003);上海市优秀学科带头人计划(09XD1401700);上海大学创新基金项目(08-22);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：数值方法研究超临界速度下轴向运动梁横向非线性振动前两阶固有频率.通过对非平凡平衡位形做坐标变换,建立超临界轴向运动梁的标准控制方程,一个积分-偏微分非线性方程.利用有限差分法数值离散梁两端简支边界下控制方程,计算轴向运动梁中点的横向振动位移,并将计算结果作为时间序列,运用离散傅立叶变换得到超临界轴向运动梁横向振动的频率.通过数值算例,讨论了系统参数对前两阶固有频率在超临界范围随轴向速度变化的影响.In the present paper,the first two supercritical natural frequencies of nonlinear transverse free vibration of axially moving beams are numerically investigated. In the supercritical transport speed re- gime,the nonlinear integro-partial-differential equation is cast in the standard form of continuous gyroscopic sys- tems via introducing a coordinate transform for the non-trivial equilibrium configuration. Numerical schemes are presented for the governing equation via the finite difference method under the simply supported boundary condi- tion. Time series of the discrete Fourier transform is defined as numerically solutions of nonlinear governing equa- tion for the first two natural frequencies of nonlinear transverse vibration. The numerical results illustrate the tendencies of the first two natural frequencies with the changing system parameters.

关 键 词：轴向运动梁 非线性 固有频率 横向振动 超临界 

分 类 号：O322[理学—一般力学与力学基础]