压电弹性厚板动力学的简化Gurtin型变分原理  

SIMPLIFIED GURTIN-TYPE VARIATIONAL PRINCIPLES FOR ELASTODYNAMICS OF PIEZOELECTRIC THICK PLATE

作　　者：朱慧坚[1] 罗恩[2] 

机构地区：[1]广东技术师范学院计算机科学系,广州51066 [2]中山大学应用力学与工程系,广州510275

出　　处：《动力学与控制学报》2007年第4期302-307,共6页Journal of Dynamics and Control

基　　金：高校博士点科研基金(20030558025);国家自然科学基金(10172097)资助项目~~

摘　　要：根据古典阴阳互补和现代对偶互补的基本思想,通过罗恩提出的一条简单而统一的新途径,系统地建立了压电弹性厚板动力学的各类简化Gurtin型变分原理.这种简化Gurtin型变分原理能反映动力学初值-边值问题的全部特征.文中首先给出压电厚板动力学的广义虚功原理的表式,然后从该式出发,不仅能得到虚功原理,而且通过所给出的一系列广义Legendre变换,还能系统地成对导出压电弹性厚板动力学的8类、6类、4类变量简化Gurtin型变分原理的互补泛函以及3类和2类变量简化Gurtin型势能形式的泛函.同时,通过这条新途径还能清楚地阐明这些原理的内在联系.According to the basic idea of classical Yin-Yang complementarity and modem dual-complementarity, in a new, simple and unified way proposed by Luo, the simplified Gurtin-type variational principles for elastodynamics of piezoelectric thick plate can be established systematically. The simplified Gurtin-type variational principles can fully characterize the initial-boundary problem of elastodynamics of piezoelectric thick plate. An important integral relation is given, which can be considered as the generalized principle of virtual work for dynamics of piezoelectric thick plate. Based on this relation, it is possible not only to obtain the principles of virtual work, but also to derive systematically the complementary functionals for eight-field, six-field, four-field simplified Gurtin-type variational principles and the potential energy functional for three-field and two-field simplified Gurtintype principle for elastodynamics of piezoelectric thick plate by the generalized Legendre transformation given in this paper . Furthermore , with this approach, the intrinsic relation among various principles can be explained clearly.

关 键 词：压电弹性厚板 动力学 简化Gurtin型变分原理 对偶互补 初值-边值问题 

分 类 号：O343[理学—固体力学]