双侧弹性约束悬臂梁的非光滑擦边动力学  

Non-Smooth Grazing Dynamics for Cantilever Beams With Bilateral Elastic Constraints

作　　者：史美娇 徐慧东 张建文 SHI Meijiao;XU Huidong;ZHANG Jianwen(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,P.R.China;College of Mechanical and Vehicle Engineering,Taiyuan University of Technology,Taiyuan 030024,P.R.China)

机构地区：[1]太原理工大学数学学院,太原030024 [2]太原理工大学机械与运载工程学院,太原030024

出　　处：《应用数学和力学》2022年第6期619-630,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11872264)。

摘　　要：研究了具有双侧弹性约束的单自由度悬臂梁系统擦边诱导的非光滑动力学行为.首先,基于弹性碰撞悬臂梁的动力学方程和擦边点的定义,分析了双侧擦边周期运动的存在性条件.其次,选取零速度的Poincaré截面,推导了双侧擦边轨道附近带参数的高阶不连续映射.然后,结合光滑流映射和高阶不连续映射建立了新的复合分段范式映射.最后,将基于低阶范式映射和高阶范式映射得到的分岔图进行对比,分析验证了高阶范式映射的有效性,并通过数值仿真进一步揭示了弹性碰撞悬臂梁的擦边动力学.The grazing-induced non-smooth dynamical behaviors of single-degree-of-freedom cantilever beam systems with bilateral elastic constraints were studied.Firstly,based on the dynamical equations for the cantilever beam under elastic impacts and the definition of grazing points,the existence condition for the bilateral grazing periodic motion was analyzed.Secondly,the zero-velocity Poincarésection was selected to derive the high-order discontinuous mapping with parameters near bilateral grazing orbits.Then a new composite piecewise normal form mapping was established through combination of the smooth flow mapping and the high-order discontinuous mapping.Finally,the validity of the high-order mapping was verified through comparison of the bifurcation diagram of the low-order mapping with that of the high-order mapping,and the grazing dynamics of the cantilever beam under elastic impacts were further revealed through numerical simulation.

关 键 词：悬臂梁 双侧弹性约束 不连续映射 擦边非光滑分岔 

分 类 号：O357.41[理学—流体力学]