受热平板振动精确化方程及其耦合响应模式分析  

Refined Governing Equations of Vibration Plate With Thermo-mechanical Coupling

作　　者：胡超[1,2] 郑日恒[3] 周传平[2] 黄文虎[4] 

机构地区：[1]扬州大学建筑科学与工程学院,扬州225127 [2]同济大学航空航天与力学学院,上海200092 [3]航天科工集团公司三十一研究所,北京100074 [4]哈尔滨工业大学航天学院,哈尔滨150001

出　　处：《中国科学：物理学、力学、天文学》2012年第10期1086-1096,共11页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:10572045,51276129);高超声速发动机技术国家重点实验室开放基金资助项目

摘　　要：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, based on the theory of thermoelastodynamics, applied the method of differential operators and the theory of gauge fields, the thermo-mechanical coupled problem of vibration plates was investigated. The refined governing equations of vibration plates and temperature including the effect of thermomechanical coupling are firstly obtained by using three gauge conditions, and the criterion representing the extent of thermomechanical coupling was given. The related some questions, for examples, the mechanism and response modes of thermo-mechanical coupling in plates were analyzed and discussed by using the theory of PDE. The proposed refined governing equations of thermo-elastic plates and its analysis results can be used to analyze and solute the thermo-mechanical dynamic problem of plates at the high temperature.

关 键 词：热弹性动力学 力热全耦合 受热平板振动精确化方程 算子方法与复变函数方法 规范条件 

分 类 号：V414.33[航空宇航科学与技术—航空宇航推进理论与工程]