黏弹性屈曲梁非线性内共振稳态周期响应

熊柳杨; 张国策; 丁虎; 陈立群

doi:10.3879/j.issn.1000-0887.2014.11.002

黏弹性屈曲梁非线性内共振稳态周期响应

doi: 10.3879/j.issn.1000-0887.2014.11.002

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;³上海市力学在能源工程中的应用重点实验室, 上海 200072

基金项目: 国家自然科学基金（重点项目）(11232009)；国家自然科学基金(11372171;11422214)；上海市教委科研创新项目(12YZ028)

详细信息

作者简介:
熊柳杨(1991—), 男, 江西宜春人, 硕士生(E-mail: xly0831@126.com);丁虎(1978—), 男,安徽明光人，研究员，博士(通讯作者. E-mail: dinghu3@shu.edu.cn).

中图分类号: O322;O345
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出版历程
- 收稿日期: 2014-05-23
- 刊出日期: 2014-11-18

Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance

¹Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200444, P.R.China;³Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China(Key Program)(11232009); The National Natural Science Foundation of China(11372171;11422214)

摘要

摘要: 研究了内共振下简支边界屈曲黏弹性梁受迫振动稳态周期幅频响应.考虑Kelvin黏弹性本构关系，并通过对非平凡平衡位形做坐标变换，建立屈曲梁横向振动的非线性偏微分-积分模型.基于对控制方程的Galerkin截断，得到多维非线性常微分方程组.在前两阶模态内共振存在的条件下，运用多尺度法分析截断后的控制方程，利用可解性条件消除长期项，获得一阶主共振下的幅值与相角方程.通过数值算例以展示系统稳态幅频响应关系以及失稳区域，从而聚焦系统共振中存在的非线性现象，如跳跃现象、滞后现象，并讨论了双跳跃现象随轴向荷载的演化.通过直接数值方法处理截断方程，数值验证近似解析解，计算结果表明多尺度法具有较高精度.
- 屈曲梁 /
- 黏弹性 /
- 内共振 /
- 多尺度方法 /
- 稳定性
Abstract: Nonlinear vibration of a hinged-hinged viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance was investigated. The governing integro-partial differential equation was derived via introduction of coordinate transform for the non-trivial equilibrium configuration, with the viscoelastic constitutive relation taken into account. Based on the Galerkin method, the governing equation was truncated to a set of infinite ordinary differential equations and the condition for internal resonance was obtained. The multiple scales method was applied to derive the modulation-phase equations. Steady-state periodic solutions to the system as well as their stability were determined. The numerical examples were focused on the nonlinear phenomena, such as double-jump and hysteresis. The generation and vanishing of a double-jumping phenomenon on the amplitude-frequency curves were discussed in detail. The Runge-Kutta method was developed to verify the accuracy of results from the multiple scales method.
- buckled beam /
- viscoelasticity /
- internal resonance /
- multiple scales method /
- stability

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参考文献(12)

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黏弹性屈曲梁非线性内共振稳态周期响应

doi: 10.3879/j.issn.1000-0887.2014.11.002

作者简介:
熊柳杨(1991—), 男, 江西宜春人, 硕士生(E-mail: xly0831@126.com);丁虎(1978—), 男,安徽明光人，研究员，博士(通讯作者. E-mail: dinghu3@shu.edu.cn).

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Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance

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黏弹性屈曲梁非线性内共振稳态周期响应

doi: 10.3879/j.issn.1000-0887.2014.11.002

作者简介: 熊柳杨(1991—), 男, 江西宜春人, 硕士生(E-mail: xly0831@126.com);丁虎(1978—), 男,安徽明光人，研究员，博士(通讯作者. E-mail: dinghu3@shu.edu.cn).

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出版历程

Steady-State Periodic Responses of a Viscoelastic Buckled Beam in Nonlinear Internal Resonance

计量

出版历程

目录

作者简介:
熊柳杨(1991—), 男, 江西宜春人, 硕士生(E-mail: xly0831@126.com);丁虎(1978—), 男,安徽明光人，研究员，博士(通讯作者. E-mail: dinghu3@shu.edu.cn).