基于等效转化关系的一维非均匀介质波动问题解析方法研究  

Analytical solutions to wave motion in a one-dimensional inhomogeneous medium based on an equivalent transformation relationship

作　　者：杨在林[1] 王耀[1] 黑宝平[1] 李志东[1] 

机构地区：[1]哈尔滨工程大学航天与建筑工程学院,哈尔滨150001

出　　处：《振动与冲击》2016年第6期152-155,共4页Journal of Vibration and Shock

基　　金：国家科技支撑计划课题(2015BAK17B06);2015年地震行业科研专项经费项目(201508026-02);黑龙江省自然科学基金(A201310);黑龙江省博士后科研启动金(LBH-Q13040);中央高校基本科研业务费专项资金资助项目(HEUCF150203)

摘　　要：基于波动方程与位移场解答等效思路,获得非均匀介质波动问题与均匀介质柱面波等效转化关系。分析发现两类问题模型间可相互转化,问题解答可相互等效。等效转化实质为几何形状与材料参数的等效关系。利用等效转化关系获得两个一维非均匀介质波动问题算例的解析解。Based on the idea of the equivalent wave motion equation and the equivalent displacement field solution, the equivalent transformation relationship was obtained between the wave in the 1D inhomogeneous medium and the cylindrical wave in the homogeneous medium. Each model can be transformed equivalently into the other. The solutions of these two problems are equivalent to each other. The nature of the equivalent transformation is the equivalent relationship between geometry and material parameters. According to the relationship, analytic solutions were obtained for two examples of the wa^e motion problems in the 1 D inhomogeneous medium in this work.

关 键 词：非均匀介质 波动 等效转化 

分 类 号：O343.7[理学—固体力学]