Research On Time Domain Boundary Element Method Associated With Its Instability For Non-stationary Sound Field Prediction And Reconstruction

The boundary element method(BEM)is developed succeeding the finite element method(FEM).Compared to FEM,the BEM only requires discretization of the boundary of the analysis domain,which leads to less elements and a simpler preprocess.In addition,the character that it automatically satisfies the Sommerfeld radiation condition makes it superior to FEM in solving radiation problems in infinite domain.The BEM can be categorized to frequency domain BEM(FBEM)and time domain BEM(TBEM)according to the signal type.The FBEM has been utilized in acoustic radiation problems since 1960 s.It was getting more popular as it was improving in other subjects,such as elastics,elastodynamics,structure mechanics and so on.However,the FBEM is only suitable for stationary problems.For non-stationary problems,people usually turns to the TBEM.The TBEM is also known as the time domain boundary integral equation method or the retarded potential integral equation method.It is well-known that the TBEM suffers from instability problems which prevent this method from being used widely.This dissertation further discussed the instability problem of TBEM.The stability influence of the temporal basis functions was studied and better choices were suggested.To implement the TBEM in practical engineering problems,a Burton-Miller-type TBEM in half-space(BMHS-TBEM)was developed.The horn effect of a tire was studied through the BMHS-TBEM.After deeply understanding the theory of TBEM,the theory of inverse TBEM(ITBEM)for non-stationary sound field reconstruction was then established.Moreover,the stability analysis of ITBEM was also conducted through an eigenvalue system.The detailed researches are given below:In chapter one,the background of this research was provided,and an introduction of FBEM and TBEM was presented.The development of NS-NAH was also introduced.Based on the deep understand of the existing methods,the main subject of this dissertation was decided.Chapter two gave the basic theory of TBEM.Apart from the basic theory,the stability influence of the temporal basis functions was also studied,and better choices for more stable results were suggested,which further enhanced the stability of TBEM.In chapter three,the BMHS-TBEM was proposed for solving practical problems in engineering.The BMHS-TBEM was validated through numerical examples and an experiment.Finally,the BMHS-TBEM was utilized to predict the horn effect of a tire.In chapter four,the ITBEM theory was proposed for non-stationary sound field reconstruction.The ITBEM was validated through three numerical examples and an experiment,and it was shown that the method was robust in reconstructing non-stationary sound field.Chapter five further studied the stability of TBEM and ITBEM.The formulation of ITBEM was transformed to an iterative format which contains an iterative matrix.By analyzing the eigenvalues of the iterative matrix,the stability of ITBEM can be known.The TSVD method was also incorporated in the eigenvalue system,thus by analyzing the eigenvalues,the stability mechanism of TSVD was also revealed.To further stabilize the ITBEM,an averaging method was introduced.It was shown that by using the TSVD and the averaging method,the ITBEM can meet the stability condition more easily.The research results of this dissertation were summarized in chapter six.The potential subjects which were meaningful but not mentioned in this dissertation were given.