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工程科学与技术:2008,40(5):7-12
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粘弹性板热机耦合非线性振动(Ⅰ)——动力学模型
(西南交通大学 应用力学与工程系,四川 成都 610031)
Nonlinear Vibration of a Thermo-mechanical Coupling Viscoelastic Plate (Ⅰ)——Dynamical Model
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投稿时间:2007-12-10    
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。
Abstract: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
文章编号:20080502     中图分类号:    文献标志码:
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)
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李映辉,王燕楠,邓一三.粘弹性板热机耦合非线性振动(Ⅰ)——动力学模型[J].工程科学与技术,2008,40(5):7-12.
.Nonlinear Vibration of a Thermo-mechanical Coupling Viscoelastic Plate (Ⅰ)——Dynamical Model[J].Advanced Engineering Sciences,2008,40(5):7-12.