非均匀弹簧界面模型下柱形夹杂物对弹性波的散射  

ELASTIC WAVE SCATTERING OF A CYLINDER BASED ON INHOMOGENEOUS INTERFACE SPRING MODEL

作　　者：刘希强[1] 魏培君[1] 

机构地区：[1]北京科技大学应用科学学院数力系,北京100083

出　　处：《工程力学》2008年第2期83-87,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(10272003;10672019);北京科技大学引进人才基金

摘　　要：利用波函数展开法研究了非均匀弹簧界面模型(弹簧系数沿周向非均匀分布)下单个柱形夹杂物对弹性波的散射问题。在弹簧界面模型中,当弹簧系数沿周向分布均匀时,可利用波函数的正交性简化边界条件;当弹簧系数沿周向分布不均匀时,不能利用波函数的正交性简化边界条件。该文研究了这一问题,通过沿周向的离散化将弹性波散射的边界条件归结为一个超定线性代数方程组。针对Ge-Al纤维增强复合材料数值计算了散射截面和远场散射幅。特别地,通过适当选取弹簧常数的周向分布处理了含裂纹界面的弹性波散射问题,数值计算了裂纹张开位移和错开位移。The elastic wave scattering of a cylinder with inhomogeneous interface properties is studied by use of wave function expansion method. When the spring coefficient in the interface spring model is homogeneous along circumference, the orthogonal properties of wave functions can be used to simplify the boundary conditions. However, the orthogonal properties of wave functions can not be used to simplify the boundary conditions when the spring coefficient in the interface spring model is inhomogeneous along the circumference. In order to determine the unknown expansion coefficients, the discretization along the circumference is used and a linear algebraic equation set is derived. The numerical simulation is carried .out for the composites Ge-Al. Both scattering cross-section and far-field scattering amplitude are computed. In addition, the scattering problem of a cylinder with local debond can be solved in the present inhomogeneous interface spring model by assuming that the spring coefficients at the debond region are equal to zero. The displacement jumps （open and slip displacement） at the debond region （local crack） are computed in the numerical example.

关 键 词：弹簧模型 弹性波散射 界面裂纹 散射截面 远场散射幅 

分 类 号：O347.41[理学—固体力学]