含热传导效应粘弹性板耦合非线性动力分析模型  

Nonlinear Dynamic Model of a Thermo-Mechanical Coupling Viscoelastic Plate with the Influence of Thermal Conduction

作　　者：王燕楠[1] 李映辉[1] 邓一三[1] 

机构地区：[1]西南交通大学应用力学与工程系,四川成都610031

出　　处：《西华师范大学学报（自然科学版）》2008年第2期117-121,共5页Journal of China West Normal University(Natural Sciences)

基　　金：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项目(2006B03)

摘　　要：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,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.且该热机耦合非线性动力学模型可以退化为粘弹性板动力学模型、仅含热膨胀效应粘弹性板动力学模型和热机耦合弹性板动力学模型.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, in consideration of the influence of thermal conduction, is obtained by means of the constitutive description of thermo-viscoelastic material obeyed by the Bohzmann＇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 can be converted to a nonlinear differentialintegral dynamical system by using Galerkin＇s method. The dynamic model of the visco-elastic plate and the viscoelastic plate with the influent of heat expansion and the thermo-mechanical coupling dynamic model of elastic plate which can be obtained from the system are the same with the corresponding models from [ 1,2,8].

关 键 词：热传导 粘弹性板 耦合 非线性动力模型 

分 类 号：O342.6[理学—固体力学]