轴向运动三参数黏弹性梁的分岔与混沌

doi:10.12066/j.issn.1007-2861.1870

上海大学学报(自然科学版) ›› 2018, Vol. 24 ›› Issue (5): 713-720.doi: 10.12066/j.issn.1007-2861.1870

轴向运动三参数黏弹性梁的分岔与混沌

李怡¹, 严巧赟¹, 丁虎¹(), 陈立群¹^,²

1. 上海大学上海市应用数学和力学研究所, 上海 200072
2. 上海大学理学院, 上海200444

收稿日期:2016-11-14 出版日期:2018-10-30 发布日期:2018-10-26
通讯作者: 丁虎 E-mail:dinghu3@shu.edu.cn
基金资助:
国家自然科学基金重点资助项目(11232009);国家自然科学基金面上资助项目(11372171);国家自然科学基金优青资助项目(11422214)

Bifurcation and chaos of axially moving viscoelastic beam constituted by standard linear solid model

LI Yi¹, YAN Qiaoyun¹, DING Hu¹(), CHEN Liqun¹^,²

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
2. College of Sciences, Shanghai University, Shanghai 200444, China

Received:2016-11-14 Online:2018-10-30 Published:2018-10-26
Contact: DING Hu E-mail:dinghu3@shu.edu.cn

摘要/Abstract

摘要：

研究了轴向运动黏弹性梁在参数激励下的非线性动力学行为. 采用牛顿第二定律推导了轴向运动梁的积分-偏微分控制方程, 采用三参数模型本构关系描述了运动梁的黏性特征. 运用四阶Galerkin截断方法将控制方程离散为常微分方程组, 并采用四阶Runge-Kutta法对常微分方程组求解, 得到了运动梁上各点的时间响应历程, 进而分析了运动梁的分岔与混沌特征. 通过时间历程图以及频谱分析图、相图、庞加莱映射图, 呈现了系统的混沌现象. 着重考察了三参数黏弹性对系统非线性动力学行为的影响. 结果发现, 轴向运动梁的非线性振动对黏弹性各个参数都很敏感.

关键词: 轴向运动梁, 三参数模型, Galerkin截断, 分岔, 混沌

Abstract:

The nonlinear dynamic behavior of an axially moving viscoelastic beam under parametric excitation is investigated. A standard linear solid model is used in the constitutive relation. Newton's second law is applied to derive a nonlinear integral-partial-differential governing equation of the beam. The fourth-order Galerkin truncation method is applied to truncate the governing equation into a set of ordinary differential equations solved with the fourth-order Runge-Kutta method. Based on the diagrams of time history, phase, Poincaré map and frequency analysis, the dynamical behavior is identified. The investigation is focused on the effects of the standard linear solid model's viscoelasticity on the nonlinear dynamic behavior. Numerical simulations show that vibration of an axially accelerating viscoelastic beam is sensitive to all parameters of the standard linear solid model.

Key words: axially moving beam, standard linear solid model, Galerkin truncation, bifurcation, chaos

中图分类号:

O322

李怡, 严巧赟, 丁虎, 陈立群. 轴向运动三参数黏弹性梁的分岔与混沌[J]. 上海大学学报(自然科学版), 2018, 24(5): 713-720.

LI Yi, YAN Qiaoyun, DING Hu, CHEN Liqun. Bifurcation and chaos of axially moving viscoelastic beam constituted by standard linear solid model[J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(5): 713-720.

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轴向运动三参数黏弹性梁的分岔与混沌

Bifurcation and chaos of axially moving viscoelastic beam constituted by standard linear solid model

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