Acoustic Sensitivity Analysis Based On 2.5-dimensional Singular Boundary Method

With the rapid development of the transportation industry,the problem of traffic noise pollution has gradually attracted the attention of the public.As the most important environmental noise source,traffic noise has a great impact on people’s physical and mental health.In order to reduce the harm which caused by noise,the first thing to do is to use numerical calculation method to simulate and predict the sound field.In road and rail transit systems,the involved computational domains are mostly infinite and semi-infinite domains,and the boundary method is more suitable for solving such problems.So,the singular boundary method(SBM)which only needs boundary discretization is adopted in this paper.This method does not need mesh generation and programming is simple.The fundamental solution satisfying the governing equation is introduced as the kernel function,which automatically satisfies the Sommerfeld radiation condition and can be directly used to solve the infinite domain and semiinfinite domain problems.However,the interpolation matrix of the SBM is a full rank matrix,and the calculation of the coefficient matrix for solving the whole space and half space problems is very expensive.In this paper,a 2.5D SBM is established for the geometric invariant crosssection commonly used in road and rail transit systems to overcome the problem of large computational consumption of the traditional SBM in dealing with such models.The main work of this paper is as follows:(1)The technical route of SBM for solving acoustic problems is given.The origin intensity factor(OIF)is proposed to isolate the singular terms.Some methods are proposed to obtain the OIFs.The numerical implementation of SBM is formulated.The feasibility of the SBM is presented in solving acoustic propagation problems,which meanwhile reveals the expensive computational cost of the SBM in large-scale problems.(2)A 2.5D SBM is proposed to deal with 3D acoustic problems.Taking advantages of the geometrical invariant cross-section of the structure,the 3D problem is transformed into a series of 2D problems by Fourier transform,and the 2D problem is solved by the SBM.Finally,3D solutions are obtained from 2D solutions via inverse Fourier transform.Numerical examples validate the accuracy and effectiveness of the proposed algorithm.Compared with the traditional 3D SBM,the efficiency of the proposed algorithm is verified.(3)Based on the full space algorithm with the fundamental solution and the OIFs of the half-space problem,a half-space 2.5D SBM is proposed.Numerical examples verify the accuracy and efficiency of the 2.5D SBM.(4)Based on the direct differential method,the 2.5D SBM is extended to acoustic sensitivity analysis,where the fundamental solution and OIFs are derived.The accuracy of the method is verified by numerical examples with respect to wavenumber and structural size as design variable.The proposed method is readily applied to the structural acoustic optimization problems.