一种新的声椭球无限单元  

A Novel Ellipsoidal Acoustic Infinite Element

作　　者：杨瑞梁[1] 汪鸿振[2] 

机构地区：[1]中原工学院能源与环境工程系,郑州450007 [2]上海交通大学振动冲击噪声国家重点实验室,上海200030

出　　处：《应用数学和力学》2005年第2期239-245,共7页Applied Mathematics and Mechanics

摘　　要：　提出了一种新的声椭球无限单元·　这种声无限单元基于一种新的声压表达式,这种声压表达式能够更准确地代表着椭球声场的声传播模式·　这种新方法的形函数类似于Burnett方法,而权函数定义为形函数和一个附加因子的乘积·　因为仅需要一维的数值积分,这种新方法的代码生成十分容易,就像处理一维单元一样·　耦合标准的有限元程序,这种声无限单元理论上能够高效地求解任何形状的声源的声辐射和声散射现象·　简要地推导了这种新方法,并给出了这种方法详尽的推导结果·　为更有效地检验该无限元方法的可行性,文中例子仅考虑无限元求解的精度,而不包括相应的有限元·　使用这种新方法。A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar to the Burnett's method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently,in the examples the infinite elements were considered,excluding the finite elements relative. This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.

关 键 词：无限元 椭球声无限元 形函数 权函数 椭球坐标 Burntt方法 

分 类 号：O422.7[理学—声学]