面内平动黏弹性板非线性振动的内-外联合共振  

Internal-External Combination Resonance of Nonlinear Vibration of in-Plane Translating Viscoelastic Plates

作　　者：唐有绮[1] 陈立群[2,3] 

机构地区：[1]上海应用技术学院机械工程学院,上海201418 [2]上海大学力学系,上海200444 [3]上海市应用数学和力学研究所,上海200072

出　　处：《应用数学和力学》2013年第5期480-487,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(青年)资助项目(11202135);上海高校青年教师培养资助计划资助项目(ZZyyy12035)

摘　　要：研究了同时存在受迫共振和1∶3内共振时的面内平动黏弹性板的横向非线性振动问题.板的黏弹性材料用Kelvin本构关系描述.基于系统的运动方程和四边简支的边界条件,对偏微分方程应用直接多尺度法建立了联合共振时的可解性条件.应用Routh-Hurvitz判据对系统幅频响应的稳定性进行了判别.给出了黏弹性系数、面内平动速度和激励幅值3个参数对幅频响应的影响.最后,应用微分求积数值方法验证了近似解析方法的结论.Nonlinear vibrations of in-plane translating viscoelastic plates were investigated on the steady-state responses in external and internal resonances. The plate＇ s material obeyed the Kelvin model in which the material time derivative was used. Based on the governing equation and boundary conditions for four edges simple supports, the method of multiple scales was ap-plied to establish the solvability conditions in the primary resonance and the 1 ： 3 internal reso- nance. The Routh-Hurvitz criterion was used to determine the stabilities of the steady-state re-sponses. The effects of the viscosity coefficient, the in-plane translating speed, and the excita-tion amplitude on the steady-state responses were examined. The differential quadrature scheme was developed for the plate model to solve the nonlinear governing equations numeri-cally. The numerical calculations confirm the approximate analytical results regarding the solu-tions of the steady-state responses.

关 键 词：面内平动板 黏弹性 受迫振动 内共振 多尺度法 微分求积法 

分 类 号：O316[理学—一般力学与力学基础]