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本文于三维热弹性动力学,采用微分算子方法和规范场理论,研究了平板构振动的力热耦合问题.选取适当的规范条件,实现了弹性变形场与温度场的耦,分别推出了受热平板热弹性弯曲振动的精确化方程和温度支配方程,并给出了描述力热耦合程度的无量纲判据.而后,于偏微分方程种类和的构造理论对受热平板构内力热耦合制和力热耦合响应模式等问题做了分析讨论.给出的平板构热弹性振动精确化方程及其分析果,可用于求高温下平板构内应力场和温度场都是动态变化的耦合问题.
In this paper, three-dimensional thermo-elastic dynamics are studied, and the problem of force and heat coupling of plate vibration is studied by using the differential operator method and the gauge field theory. Coupling the elastic deformation field with the temperature field, The exact equation and the temperature governing equation for thermo-elastic bending of plate are given and the dimensionless criterion describing the degree of thermo-mechanical coupling is given. Then, the theory of the structure of partial differential equations and the theory of thermo- Heat-coupled response mode and other issues are discussed and discussed.At the same time, the exact equations and their analysis of the thermostatic elastic vibration of the plate structure can be used to solve the problem that the stress field and the temperature field in the plate structure are dynamically changing under high temperature.