Acoustic Sensitivity Analysis Of Vehicles And Noise Barriers Based On Meshless Singular Boundary Metho

Acoustic sensitivity analysis plays a significant role in the low-noise design of vehicles and the structural optimization of sound barriers.Acoustic sensitivity analysis of vehicles products is crucial in reducing noise radiation,lowering development costs,shortening development cycles,enhancing product competitiveness,and providing direction and quantitative basis for acoustic performance optimization,among other aspects.In the design process of sound barriers,performing acoustic sensitivity analysis on the barriers allows the identification of the optimal shape through numerical simulation,providing data support and production guidance for actual product manufacturing.The singular boundary method,an accurate semi-analytical meshless method,offers genuine meshless characteristics,no integration,mathematical simplicity,and ease of programming.This method employs the fundamental solution that satisfies the acoustic Helmholtz equation,which automatically meets the Sommerfeld radiation boundary condition at infinity,facilitating numerical simulations of external acoustic problems such as acoustic sensitivity for vehicles and sound barriers.In this paper,based on the meshless singular boundary method,the acoustic sensitivity calculation formula was theoretically derived,and a novel semi-analytical numerical calculation model for acoustic sensitivity analysis of vehicles and sound barriers was established.Using Matlab as the programming tool,two-dimensional and three-dimensional benchmark examples analysis programs were developed,validating the effectiveness,accuracy,and stability of the method.Subsequently,the acoustic sensitivity of vehicles and sound barriers was analyzed.This work provides a simple and efficient numerical calculation tool for the acoustic structural optimization design of vehicles and sound barriers.The main content of this paper are as follows:First of all,based on the ideas of the singular boundary method and the direct differentiation method,the meshless singular boundary method formula for acoustic sensitivity analysis was theoretically derived.Additionally,the Burton-Miller-type acoustic sensitivity formula was further derived to address the virtual frequency issue,effectively avoiding the virtual frequency problem in the simulation of infinite domain acoustic fields.A simple and efficient set of numerical calculation formulas was established,and the effectiveness and computational accuracy of the algorithm were validated through twodimensional and three-dimensional benchmark examples.Secondly,by combining the Burton-Miller-type singular boundary method with the adjoint variable method,a novel semi-analytical approach for acoustic sensitivity analysis was derived.Compared to the direct differentiation method,the adjoint variable method introduces an adjoint matrix,eliminating the need for repeated calculations of the coefficient matrix when analyzing design variables unrelated to the coefficient matrix.This can save computational time and computer resources.The effectiveness and accuracy of the developed method were demonstrated through numerical examples.Finally,a matrix decomposition technique was introduced into the singular boundary method,resulting in the development of a fast computational method for acoustic sensitivity analysis.The established fast algorithm effectively reduces the computer memory occupied and increases the computational scale.Compared to the traditional singular boundary method,the newly developed method can easily implement acoustic simulations with tens of thousands or even hundreds of thousands of degrees of freedom on a standard computer.By conducting acoustic sensitivity analysis on automobile models and sound barriers,it was demonstrated that the proposed method can significantly improve computational speed and increase the computational scale while ensuring accuracy.