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论文摘要

粘弹性板热机耦合非线性振动(Ⅱ) ——数值方法及结果

Nonlinear Vibration of a Thermo-mechanical Coupling Viscoelastic Plate (Ⅱ)——Numerical Method and Results

作者:王燕楠(西南交通大学 力学与工程学院 四川 成都 610031);李映辉(西南交通大学 力学与工程学院 四川 成都 610031);邓一三(西南交通大学 力学与工程学院 四川 成都 610031)

Author:(School of Mechanics and Eng., Southwest Jiaotong Univ., Chengdu 610031, China);(School of Mechanics and Eng., Southwest Jiaotong Univ., Chengdu 610031, China);(School of Mechanics and Eng., Southwest Jiaotong Univ., Chengdu 610031, China)

收稿日期:2007-12-10          年卷(期)页码:2008,40(6):69-74

期刊名称:工程科学与技术

Journal Name:Advanced Engineering Sciences

关键字:粘弹性板;热效应;耦合;超混沌;分岔

Key words:viscoelastic plate; thermal effect; thermo mechanical coupling; hyperchaos; bifurcation

基金项目:国家自然科学基金资助项目(10472097);西南交通大学科研基金(2006B03)

中文摘要

基于粘弹性板热机耦合非线性积分-微分动力学模型,通过引入差分得到了粘弹性板普遍适用的非线性数值计算方法,然后对一类特殊的热机耦合动力学模型进行了求解,最后综合利用非线性动力学中的数值分析方法,揭示了粘弹性矩形板的热机耦合非线性动力学行为。研究表明:热机耦合粘弹性矩形板在横向周期激励和面内均布力作用下具有十分丰富的动力学行为,比不考虑温度效应的粘弹性板的混沌性更强,还出现了超混沌现象。

英文摘要

Based on the nonlinear integral ordinary differential dynamical system of the thermo mechanical coupling viscoelastic plate, the general nonlinear numerical method for viscoelastic plate was obtained by introducing difference method. A kind of special dynamic model with thermo mechanical coupling was solved. Finally, synthetically using several methods in dynamic systems, the dynamic properties of the thermo mechanical coupling viscoelastic plate were sufficiently revealed. It was found that the dynamic properties of the thermo mechanical coupling viscoelastic plate subjected to both actions of an alternating periodic transverse external excitation and in plane uniform distributed force are abundant, and the chaos is greater than the viscoelastic plate’s without the influence of temperature, especially, the motion state of hyperchaos appears.

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