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)

[1]	叶敏, 陈予恕. 弹性屈曲梁在参数激励下的倍周期分叉[J]. 固体力学学报, 1998,19(4): 361-364.(YE Min, CHEN Yu-shu. Period doubling bifurcation in elastic buckled beam under parametric excitation[J]. Acta Mechnica Solida Sinica,1998,19(4): 361-364.(in Chinese))
[2]	朱媛媛, 胡育佳, 程昌钧. Euler型梁-柱结构的非线性稳定性和后屈曲分析[J]. 应用数学和力学, 2011,32(6): 674-682.(ZHU Yuan-yuan, HU Yu-jia, CHENG Chang-jun. Analysis of nonlinear stability and post buckling for the Euler-type beam-column structure[J]. Applied Mathematics and Mechanics,2011,32(6): 674-682.(in Chinese))
[3]	王昊, 陈立群. 强横向激励作用下屈曲梁的稳态幅频响应特性[J]. 应用数学和力学, 2014,35(2): 181-187.(WANG Hao, CHEN Li-qun. Steady-state amplitude-frequency characteristics of axially buckled beams under strong transverse excitation[J]. Applied Mathematics and Mechanics,2014,35(2): 181-187.(in Chinese))
[4]	Lacarbonara W, Nayfeh A H, Kreider W. Experimental validation of reduction methods for nonlinear vibrations of distributed-parameter systems: analysis of a buckled beam[J]. Nonlinear Dynamics,1998,17(2): 95-117.
[5]	Emam S A, Nayfeh A H. On the nonlinear dynamics of a buckled beam subjected to a primary-resonance excitation[J]. Nonlinear Dynamics,2004,35(1): 1-17.
[6]	Nayfeh A H, Balachandran B. Modal interactions in dynamical and structural systems[J]. Applied Mechanics Reviews,1989,42(11): 175-201.
[7]	Afaneh A, Ibrahim R. Nonlinear response of an initially buckled beam with 1∶1 internal resonance to sinusoidal excitation[J]. Nonlinear Dynamics,1993,4(6): 547-571.
[8]	Chin C M, Nayfeh A H, Lacarbonara W. Two-to-one internal resonances in parametrically excited buckled beams[C]// Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference,1997: 213-223.
[9]	陈宁. 屈曲非线性黏弹性梁的动力学行为研究[J]. 力学学报, 2002,34(增刊): 229-233.(CHEN Ning. Dynamical behaviors of nonlinear viscoelastic buckled beams[J]. Acta Mechanica Sinica,2002,34(S): 229-233.(in Chinese))
[10]	Xiong L Y, Zhang G C, Ding H, Chen L Q. Nonlinear forced vibration of a viscoelastic buckled beam with 2∶1 internal resonance[J]. Mathematical Problems in Engineering,2014,2014. Article ID 906324.
[11]	Nayfeh A H, Emam S A. Exact solution and stability of postbuckling configurations of beams[J]. Nonlinear Dynamics,2008,54(4): 395-408.
[12]	Chen L Q, Zhang Y L, Zhang G C, Ding H. Evolution of the double-jumping in pipes conveying fluid flowing at the supercritical speed[J]. International Journal of Non-Linear Mechanics,2014,58: 11-21.

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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).