Acoustic Analysis of Multi-domain and Thin-body Problems

本课题利用积分方程的方法来制定和解决声学中几种类型的多域和薄体问题。对于多域问题，感兴趣的声学域是任意形状的封闭表面的内部，封闭体的外部，或耦合到另一个域。对于薄体问题，声域位于最小尺寸与单元长度等数值参数相同或小于某些数值参数的物体的外部。利用积分方程方法，所有的数值逼近都被限制在域的边界上。不需要将区域内部离散化，因此问题的计算维度减少了一个（三维问题在区域的二维边界上解决），并且没有与有限元方法相关的困难，例如，决定在声学介质中停止元件的位置。因此，使用积分方程解决多域问题比需要解决整个域的替代技术更简单、更准确。多域和薄体声学问题的解决方法的发展将有利于广泛的具体工程问题。其中包括预测发动机、泵和压缩机等工业产品在部分被噪声控制外壳覆盖时的声压和辐射功率；车辆和飞机的安静内饰设计；了解如何在主动振动/主动噪声控制中使用多个源；以及复杂的声通道网络的设计和优化，例如消声器、发动机诱导系统和风扇消声器内部的声通道网络。

This project utilizes the integral equation method to formulate and solve several types of multi-domain and thin-body problems in acoustics. For the multi-domain problem, the acoustic domain of interest is interior to a closed surface of arbitrary shape, exterior to a closed body, or coupled to another domain. For the thin body problem, the acoustic domain is exterior to a body whose smallest dimension is of the same order or less than some numerical parameter such as element length. By using integral equation methods, all numerical approximations are confined to the boundaries of the domains. There is no need to discretize the interior of the domain, and therefore a reduction in the computational dimension of the problem by one (three dimensional problems are solved on the two dimensional boundary of the domain), and there is none of the difficulty associated with finite element methods, for example, of deciding where in the acoustic medium to stop the elements. It is thereby potentially simpler and more accurate to solve multi-domain problems using integral equations than alternative techniques requiring solution throughout the domains. The development of methods for the solution of multi-domain and thin-body acoustic problems will be beneficial to a wide range of specific engineering problems. These include the prediction of sound pressure and power radiated by industrial products such as engines, pumps and compressors when partially shrouded by an enclosure for noise control; design of quiet interiors of vehicles and aircraft; understanding how multiple sources may be used in active vibration/active noise control; and the design and optimization of complex networks of acoustic passageways such as those that occur in the interior of mufflers, induction systems of engines and silencers for fans.