粘弹性板热机耦合非线性振动（Ⅰ）——动力学模型
Nonlinear Vibration of a Thermo-mechanical Coupling Viscoelastic Plate （Ⅰ）——Dynamical Model
作者：李映辉(西南交通大学 应用力学与工程系,四川 成都 610031)；王燕楠(西南交通大学 应用力学与工程系,四川 成都 610031)；邓一三(西南交通大学 应用力学与工程系,四川 成都 610031)
Author：(Dept. of Applied Mechanics and Eng., Southwest Jiaotong Univ., Chengdu 610031, China)；(Dept. of Applied Mechanics and Eng., Southwest Jiaotong Univ., Chengdu 610031, China)；(Dept. of Applied Mechanics and Eng., Southwest Jiaotong Univ., Chengdu 610031, China)
收稿日期：2007-12-10 年卷（期）页码：2008,40(5):7-12
期刊名称：工程科学与技术
Journal Name：Advanced Engineering Sciences
关键字：粘弹性板；热机耦合；微分-积分动力系统； 非线性动力模型
Key words：viscoelastic plate;thermo-mechanical coupling;differential-integral dynamical system;nonlinear dynamic model
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资助（2006B03）
中文摘要
建立了横向周期荷载、面内均布荷载和温度场作用下，考虑热传导效应的粘弹性矩形板的热机耦合非线性动力学模型。基于薄板大挠度Karman理论和用Boltzmann叠加原理描述的粘弹性材料本构方程、动力学平衡方程和热粘弹能量原理建立了考虑热传导效应的粘弹性矩形板的热机耦合非线性动力学模型，并用Galerkin方法将该热机耦合非线性动力学模型转化为非线性微分－积分动力系统。研究表明：1)在热传导系数和热膨胀都为0时，该热机耦合非线性动力学模型退化为粘弹性板动力学模型；2)在热传导系数为0而热膨胀不为0时，该热机耦合动力学模型简化为仅考虑热膨胀时的粘弹性板动力学模型；3) 当材料的粘性项为0时，即动力学模型中积分项为0时，该热机耦合动力学模型退化为热机耦合弹性板动力学模型。
英文摘要
The nonlinear dynamic model of a thermo-mechanical coupling viscoelastic rectangular plate with temperature field and subjected to both actions of an alternating periodic transverse external excitation and in plane uniform distributed force is established.The model,which talce into account of the influence of thermal conduction,is obtained by means of the constitutive description of thermo-viscoelastic material obeying the Boltzman’s superposition principle and the dynamic equilibrium equation of the rectangular plate on the basis of the Karman theory for thin plates with large deflection and the thermo-viscoelastic energy theory.It may be converted to a nonlinear differential integral dynamic system by using Galerkin’s method.The study indicates that:1) If the effect of heat expand and thermal conduction are ignored, the model can be reduced to the one of the viscoelastic plate；2) Letting the thermal conductive coefficient be zero and the heat expand coefficient being not equal to zero,the model is the same as the dynamic model of a viscoelastic plate with the influent of heat expand;3) If the effect of viscosity is ignored,namely,the model does not include the integral items,the model can be simplified to the thermo-mechanical coupling dynamic model of elastic plate
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