Investigation On Wave Superposition Method And Meshfree Method In Computing Acoustic Field In Infinite Domain

The wave superposition method and the meshfree method for computing acoustic field in infinite domain are investigated.The prediction accuracy of acoustic pressure in the wave superposition method is affected by the locations of equivalent sources,the calculation frequency and the vibration velocity distribution on boundary.It is difficulty for the meshfree method to discretize the infinite domain and establish the system equation for predicting the acoustic pressure.To solve these problems,a comprehensive research is carried out in this dissertation.(1)The singularity,strongly singularity and hypersingular problems of the Green function when the sound source and a receiver point coincideded are investigated using the element free method.Non-singular expressions for self-radiation terms including acoustic pressure and velocity are obtained by deducing.It is studied whether the approximate analytical expressions can be used to replace the diagonal terms of the revevant matrices for computing acoustic field.(2)The interpolation function of vibration velocity is deducted and investigated.The mathematical analysis indicates that there are vibration velocity reconstruction errors in some points on the boundary,where the imaginary component of the interpolation function is not equal to zero,when the vibration velocity is evaluated using the predicted acoustic pressure.Then the relationship between the error of the predicted acoustic pressure and the vibration velocity reconstruction error on the boundary is studied and obtained by deducting.It indicates that the prediction accuracy can be improved by decreasing the vibration velocity reconstruction error.Based on these findings,a method to determine the optimal locations by minimizing the normalized vibration velocity reconstruction error is proposed to decrease the prediction error.The validity of this method is verified by simulation and experiment.(3)In the determined optimal locations,the influence of the calculation frequency on the acoustic pressure prediction accuracy is investigated for certain number of equivalent souces.The upper limiting frequency is determined by deducting and can be used to ensure the prediction accuracy of acoustic pressure.The relationship between the prediction accuracy of acoustic pressure and the vibration velocity distribution shows that the prediction accuracy can be ensured for a given vibration velocitydistribution using enough nodes determined by setting a proper threshold of dimensionless velocity reconstruction error,which is taken as 1%.(4)To improve the computational efficiency in frequency range,the stiffness matrix of the variable order acoustic wave envelope element is decomposed according to its characteristics to make the stiffness matrix independent on the frequency.A hybrid adaptive Gauss integral algorithm is proposed to ensure the accuracy and efficiency to accurately calculate the matrix elements which have great effect on the prediction accuracy of the pressure.(5)The coupling of the meshfree method with the variable-order infinite acoustic wave envelope element(WEE)method is investigated and achieved by constructing the hybrid acoustic pressure shape function of continuity and compatibility on the interface.Then,a coupled meshfree based on weak-forms and WEE method is proposed to make use of their advantages while evading their disadvantages.The mesh reconstruction in the conventional method of the finite element coupled with the WEE is canceled in the proposed method.(6)The available ranges of the dimensionless size of the influence domain and the shape parameters included in the weight functions and basis functions are investigated and determined by numerical experiments,which provides an available reference for simulation and practical acoustic field prediction.The simulation results show that the coupled method not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the WEE.The feasibility and validity of the coupled method is verified by experiments.