面内平动黏弹性板非线性振动的内-外联合共振

唐有绮; 陈立群

doi:10.3879/j.issn.1000-0887.2013.05.006

面内平动黏弹性板非线性振动的内-外联合共振

doi: 10.3879/j.issn.1000-0887.2013.05.006

唐有绮¹,
陈立群^2,3

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

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

详细信息

作者简介:
唐有绮（1984—），男，上海人，讲师，博士，硕士生导师 (通讯作者.Tel：+86-21-60873024; E-mail: tangyouqi2000@163.com).

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- 文章访问数: 1583
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- PDF下载量: 1075
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出版历程
- 收稿日期: 2013-04-02
- 修回日期: 2013-04-20
- 刊出日期: 2013-05-15

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

TANG You-qi¹,
CHEN Li-qun^2,3

¹School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200444, P.R.China;³Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072, P.R.China

摘要

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.
- 面内平动板 /
- 黏弹性 /
- 受迫振动 /
- 内共振 /
- 多尺度法 /
- 微分求积法
Abstract: Nonlinear vibrations of inplane translating viscoelastic plates were investigated on the steady-state responses in external and internal resonances. The plate’s material obeys 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 is applied to establish the solvability conditions in the primary resonance and the 3:1 internal resonance. The RouthHurvitz criterion is used to determine the stabilities of the steadystate responses. The effects of the viscosity coefficient, the in-plane translating speed, and the excitation amplitude on the steadystate responses are examined. The differential quadrature scheme is developed for the plate model to solve the nonlinear governing equations numerically. The numerical calculations confirm the approximate analytical results regarding the solutions of the steady- responses.
- in-plane translating plate /
- viscoelastic /
- forced vibration /
- internal resonance /
- method of multiple scales /
- differential quadrature scheme

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参考文献(15)

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面内平动黏弹性板非线性振动的内-外联合共振

doi: 10.3879/j.issn.1000-0887.2013.05.006

作者简介:
唐有绮（1984—），男，上海人，讲师，博士，硕士生导师 (通讯作者.Tel：+86-21-60873024; E-mail: tangyouqi2000@163.com).

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

计量

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留言板

面内平动黏弹性板非线性振动的内-外联合共振

doi: 10.3879/j.issn.1000-0887.2013.05.006

作者简介: 唐有绮（1984—），男，上海人，讲师，博士，硕士生导师 (通讯作者.Tel：+86-21-60873024; E-mail: tangyouqi2000@163.com).

计量

出版历程

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

计量

出版历程

目录

作者简介:
唐有绮（1984—），男，上海人，讲师，博士，硕士生导师 (通讯作者.Tel：+86-21-60873024; E-mail: tangyouqi2000@163.com).