论文部分内容阅读
As the traffic noise problem becomes more and more serious in the urban area, noise barrier which is the most effective method to mitigate the traffic noise has been widely applied in recent years.However, the performance of noise barrier greatly depends on its shape and surface conditions.In order to obtain optimal shape design of noise barriers, an acoustic field prediction and design sensitivity analysis algorithm is constructed in this study based on the boundary element method (BEM), and applies it to the optimization of shape parameters of noise barriers.As is well-known that the computational complexity of the conventional BEM (CBEM) is O(N3) with direct solvers, or O(N2) with appropriate iterative solvers, and the storage requirements are O(N2), where N is the degree of freedom (DOF).This drawback makes the BEM have difficulties with large models and hence be limited to numerical analysis of small bodies at low frequencies.In order to improve the efficiency of the BEM, the fast multipole method (FMM)[1] and the iterative solver GMRES[2] are employed to accelerate the computational procedure and form the fast multipole BEM (FMBEM) which can reduce both the computational complexity and storage requirement to linear or quasilinear for acoustic wave problems[3].As for the FMM approach, the wideband version technique is applied in this study, so that the present method is accurate, efficient and robust for both low-and high-frequency acoustic wave problems.Furthermore, the Burton-Miller formulation[4] is adopted to tackle the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic wave problems.Constant triangular elements are used to discretize the boundary surface so that both the strongly singular and hypersingular boundary integrals can be evaluated directly and efficiently without using any regularization technique.The gradient-based methods are employed in the optimization processes, and the gradients of performance functions with respect to design variables are calculated by using the direct differentiation method.Both 2-D and 3-D simulations of noise barriers are carried out in this study.Due to the high solution cost, the 3-D CBEM approach can only be used to simulate noise barriers with very short lengths.However, with the development of the FMBEM, long and curved barriers can now be modeled.In the numerical analysis, the performances of noise barriers with different shapes are compared first, and then the parameters of their top geometries are optimized to further improve the performances.For instance, the optimized 3D Y-shape noise barrier obtains an 3.2dB reduction of the sound pressure level at certain observation points for the frequency of 100Hz.