摘要
对功能梯度弹性半空间上覆盖一层功能梯度材料中的Love波的频散问题进行了研究,给出了Love波频散方程的一般形式.对功能梯度弹性半空间和功能梯度覆层的反平面剪切波的运动控制方程进行了求解,给出了半空间和覆盖层的位移、应力解析解,给出了Love波在该解析解下的频散方程.以覆盖层的剪切弹性模量和质量密度均呈指数函数变化,半空间的剪切弹性模量和质量密度均呈抛物线变化为例,利用迭代方法对频散方程进行了求解,给出了频散曲线.结果显示:在最低阶振型频散曲线中出现截止频率.
The dispersion of Love waves is studied in a functionally graded elastic half-space covered with a functionally graded materials layer and the general form of Love wave dispersion equation is obtained.In the functionally graded elastic half-space and the functionally graded covered layer,the motion control equations for the antiplane shear wave are solved,the analytical solutions for displacement and stress are obtained,and with these analytical solutions,the dispersion equation of Love wave is obtained.As an example,with the properties of the covered layer,the shear elastic modulus and mass density,varing gradually in exponential forms,and those of the half-space varing gradually in parabolic forms,the dispersion equations are solved by using the iteration method and the curves of dispersion are obtained.The results show that cut-off frequency appears in the dispersion curve of the lowest mode.
出处
《力学学报》
EI
CSCD
北大核心
2007年第5期678-684,共7页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(10272036).
关键词
功能梯度材料
LOVE波
波速
频散
变系数微分方程
functionally graded materials
love wave
wave velocity
dispersion
differential equation with varied coefficient
