Hamilton体系下的功能梯度电磁弹性固体内的导波研究  

GUIDED WAVES IN FGMM SOLID IN HAMILTONIAN SYSTEM

作　　者：代海涛[1] 程伟[1] 李明志[2] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100083 [2]石河子大学机械电气工程学院,新疆石河子832000

出　　处：《振动与冲击》2007年第12期79-83,116,共6页Journal of Vibration and Shock

摘　　要：根据Hamilton原理建立了三维压电压磁动力学耦合系统的Hamilton对偶体系,将经典的弹性力学一类变量问题转化为二类变量,建立了Hamilton正则方程组,研究了功能梯度电磁材料(FGMM)板/管内的弹性导波的频散特性及波结构特征。结果表明:(1)压电效应提高了Lamb波的频率和波速,而磁效应则相反,压电效应对波动的影响远大于磁效应;它们而对SH波没有影响(厚度方向极化)。(2)短路及断路电学边界条件对SH波不发生任何影响(厚度方向极化),而短路对Lamb波的频率和波速有不同程度的降低(相同波数下)。(3)在波结构上,对平板而言,所谓的"对称"和"反对称"Lamb波由于材料的梯度特性而变得不再严格的关于中心线对称或反对称。对管而言,由于材料的非均匀分布导致在轴对称扭转波模态中出现了横截面翘曲现象,轴对称纵向波也出现厚度剪切应力。The 3-dimensional coupled equations of magneto-eleetro-elastic stmctures are derived as Hamilton system by the principle of Hamilton theorem. The problem of single sort of variables is converted to that of double sorts of variables, and the Hamilton canonical equations are established. Then the frequency dispersing characters and wave structure of guided waves in functionally graded magneto-electro-elastic material( FGMM) plate and pipe are investigated. The results show: (1) The wave frequency and speed of Lamb wave are raised by piezoelectric effect but decreased by magneto-electro-elastic effect in thickness-polarized-plate while those of SH wave are not affected. The influence of piezoelectric effect on the guided waves is much greater than that of magneto-electro-elastic effect. (2) Short circuit condition can reduce the frequency and wave speed of Lamb wave under the same wave number while has no effect on those of SH wave. (3 ) The so called symmetric and antisymmetric Lamb waves are no longer symmetric and antisymmetric around the center line in the flat plate. The cross-section of the FGPM pipe is buckled in the mode of axisymmetric torsion because of nonhomo-geneity. The thickness shear stress is observed in the mode of axisymmetric longitudinal wave.

关 键 词：功能梯度压电材料 功能梯度电磁材料 HAMILTON体系 辛算法 

分 类 号：O347.1[理学—固体力学]