| Summary: | 碩士 === 國立臺灣海洋大學 === 系統工程暨造船學系 === 107 === The acoustic analysis is getting more attention for the design of product, such as electrical products and military vehicles. The precise analysis contributes to the prediction and the control of sound propagation. In this study, we introduce the iso-geometric analysis (IGA) method for three dimensional acoustic problems. We solve the Helmholtz equation in the framework of weak form to represent the sound pressure of specific frequency in space domain. The IGA method employs non-uniform rational B-splines (NURBS) as approximation function for the description of both geometric model and physical field. The NURBS function is the standard mathematical model in computer aid design (CAD). With the exact description of geometric model and the inherent high inter element continuity, IGA method is suitable for solving acoustic problems.
To construct the 3 D geometric model, we extrude the NURBS surface along a specific path. Regularized least squares method is applied for the inverse computation of control points along the path. Helmholtz equation turns into an integral equation by introducing Galerkin weak form. To perform the numerical integration, we introduce Gaussian quadrature and the divide parametric domain into sub domain of integral along the knots of knot vector. Similar to meshfree method, special treatment, penalty method, is introduced for the imposition of first type boundary conditions since the NURBS function only satisfies Kronecker delta function property at the corners of the parametric domain.
The convergence analysis of benchmark problem shows that IGA method has very high rate of convergence as the high order NURBS function is used and the improper selection of control points w
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