An Efficient Boundary Element Method Using a Modal Transformation for Transient Acoustic Problem

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In this paper, a simple and efficient boundary element method using a modal transformation is presented to solve a transient acoustic problem in the open space around a structure caused by the vibration due to the impact force on it. After the transient vibration of the structure is obtained by the finite element analysis, the velocity response of the surface of the structure is transformed to frequency domain. Transient acoustic pressures at points of interest are calculated as a combination of steady-state acoustic boundary element solutions under the velocity boundary conditions at discrete frequencies. However, high frequency terms exceeding an allowable frequency, which is decided from the boundary element mesh, are automatically omitted to obtain a stable solution while saving the computation time considerably. To get the boundary element solution effectively, a modal transformation using vibration modes of the structure is made to the boundary element matrices at each frequency, since the acoustic behavior on the surface of the structure is considered to be related deeply to that of the vibration. However, extra modes are added to express the acoustic field around the surface where displacements are fixed.Based on the present method, a boundary element transient acoustic analysis program, ASA/ACOUSTICS has been developed. Numerical examples are demonstrated.