基于带状单元法的电磁弹性多层板复频散特性分析  

ANALYSIS OF COMPLEX DISPERSION RELATION FOR MAGNETO-ELECTRO-ELASTIC,MULTILAYERED PLATE BASED ON STRIP ELEMENT METHOD

作　　者：陈江义[1] 陈花玲[2] 

机构地区：[1]郑州大学机械工程学院,郑州450001 [2]西安交通大学机械工程学院,西安710049

出　　处：《固体力学学报》2009年第2期142-147,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(50575172)资助

摘　　要：超声波在弹性介质中传播时理论上可以分为传播、非传播及衰减模式,且分别与实、虚及复波数相对应,可用复频散特性来进行描述.这一性质在电磁弹性多层板结构中同样存在.该文利用带状单元法对其进行了分析和计算.首先,利用能量守恒定律并结合介质的本构方程、平衡方程及相应边界条件构建了结构的带状单元模型,然后利用该模型获得了电磁弹性多层板的频散方程,最后以一个由压电材料BaTiO3和压磁材料CoFe2O4构成的三层板为数值分析对象,给出了波在其中传播时的复频散特性,并利用计算结果证明了当前相关文献中材料常数引用的不合理性.It is well-known that when waves travel in solid structures the motion of media is with propagation,non-propagation or evanescent modes respectively, corresponding to real, imaginary or complex wave numbers. This phenomenon can also exist in magneto-electro-elastic,multilayered structures and can be illustrated by the complex dispersion relation. In order to obtain complex dispersion relation of magneto-electro-elastic multilayered structures, the strip element method is employed in this paper. From the point of view of energy conversation, the strip element model is constructed from constitutive equations, equilibrium equations and deformation compatibility conditions of magnetic-electro-elastic media. By virtue of this model,the complex dispersion relation of a magnetic-electro-elastic, multilayered plate composed of piezoelectric material BaTiO3 and piezomagnetic CoFe2O4 is solved. The results of numerical examples correct an error about permeability of CoFe2 04 in some recent literatures. The method proposed in this paper can also be used to analyze the Green＇s functions and dynamic responses of magneto-electro-elastic, multi- layered plates.

关 键 词：带状单元法 电磁弹性材料 多层结构 频散特性 

分 类 号：O343[理学—固体力学]