National Taiwan Ocean University Research Hubhttps://scholars.ntou.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 16 Jun 2024 06:45:51 GMT2024-06-16T06:45:51Z5021Scattering of Sound from Point Sources by Multiple Circular Cylinders Using Addition Theorem and Superposition Techniquehttp://scholars.ntou.edu.tw/handle/123456789/1062Title: Scattering of Sound from Point Sources by Multiple Circular Cylinders Using Addition Theorem and Superposition Technique
Authors: Jeng-Tzong Chen; Ying-Te Lee; Yi‐Jhou Lin; I‐Lin Chen; Jia‐Wei Lee
Abstract: In this study, we use the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from point sound sources. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free‐space fundamental solution. The other is a typical boundary value problem (BVP) with specified boundary conditions derived from the addition theorem by translating the fundamental solution. Following the success of null‐field boundary integral formulation to solve the typical BVP of the Helmholtz equation with Fourier densities, the second‐part solution is easily obtained after collocating the observation point exactly on the real boundary and matching the boundary condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semianalytical solution of the Helmholtz problem. An example was demonstrated to validate the present approach. The parameter study of size and spacing between cylinders are addressed. The results are well compared with the available theoretical solutions and experimental data.
Tue, 01 Nov 2011 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10622011-11-01T00:00:00ZNull-Field Approach for Laplace Problems with Circular Boundaries Using Degenerate Kernelshttp://scholars.ntou.edu.tw/handle/123456789/2447Title: Null-Field Approach for Laplace Problems with Circular Boundaries Using Degenerate Kernels
Authors: Jeng-Tzong Chen; Wen‐Cheng Shen
Abstract: In this article, a semi‐analytical method for solving the Laplace problems with circular boundaries using the null‐field integral equation is proposed. The main gain of using the degenerate kernels is to avoid calculating the principal values. To fully utilize the geometry of circular boundary, degenerate kernels for the fundamental solution and Fourier series for boundary densities are incorporated into the null‐field integral equation. An adaptive observer system is considered to fully employ the property of degenerate kernels in the polar coordinates. A linear algebraic system is obtained without boundary discretization. By matching the boundary condition, the unknown coefficients can be determined. The present method can be seen as one kind of semianalytical approaches since error only attributes to the truncated Fourier series. For the eccentric case, vector decomposition technique for the normal and tangential directions is carefully considered in implementing the hypersingular equation in mathematical essence although we transform it to summability to divergent series. The five advantages, well‐posed linear algebraic system, principal value free, elimination of boundary‐layer effect, exponential convergence, and mesh free, are achieved. Several examples involving infinite, half‐plane, and bounded domains with circular boundaries are given to demonstrate the validity of the proposed method.
Thu, 01 Jan 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/24472009-01-01T00:00:00Z