平板弯曲自由振动的精确化动力学方程及其分析  

Refined dynamic equations of the plate bending without any assumptions

作　　者：胡超[1,2] MAFai 马兴瑞[3] 黄文虎[3] 

机构地区：[1]同济大学航空航天与力学学院,上海200092 [2]加州大学伯克利分校工程技术学院,美国伯克利94720 [3]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》2011年第6期781-790,共10页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:10572045);航天创新科学研究基金资助项目

摘　　要：该文基于弹性动力学理论,利用Boussinesq-Galerkin的弹性力学通解形式和偏微分方程的算子理论,采用了3个规范条件,建立了平板弯曲的精确化动力学方程.通过与基于三维弹性动力学和Mindlin板理论得到的频散曲线做对比,评价和考量了本文提出的平板弯曲精确化动力学方程.由于推导时没有采用任何工程假设,因此提出的平板动力学方程是较精确的,可用于分析较高频率下平板结构的振动和评价目前板弯曲振动理论的适用条件.In this paper, based on the theory of elastodynamics, applied the general solution of Boussinesq-Galerkin and the operator theory of partial differential equations, the refined dynamic equations of the plate flexural motion has been obtained by using three gauge conditions. And the dispersion relations, which are from the given theory, three dimension theory of elasticity and Mindlin’s plate theory, have been compared. The results of refined dynamic equations and applicable condition have been analyzed. Since derivation of the dynamic equation has been conducted without any assumptions, so the proposed equation of plate bending is exact, this can be used to analyze high frequency vibration of plate bending and to evaluate the applicable condition of the engineering plate theory.

关 键 词：平板弯曲波动 动力学控制方程 算子理论 规范条件 MINDLIN板理论 频散关系 解析函数 

分 类 号：O327[理学—一般力学与力学基础]