Numerical Simulation And Analysis Based On The Low-frequency Acoustic Field Characteristics

Low-frequency sound field is pervasive in people’s life, especially the low-frequency noise which does serious harm to human health. Through numerical simulation of low-frequency sound fields in the room, we can provide the necessary theory for the characteristics analysis of indoor sound field. Based on wave equation, this paper studies the inconsistent numerical simulation results of Boundary Element Method (BEM) and Morse theory in the condition of low-frequency.Firstly, to study the room acoustic wave equation of rigid boundary conditions, we establish a three dimensional BEM model and with the help of C++ program we compare BEM results with the sound pressure level results under Morse theory. Ranging from 1Hz to 1000Hz frequency, the change curve of sound pressure level indicates that there is a difference between the numerical simulation results of BEM and Morse theory when the frequency is lower than 100Hz. Hence, in the range of 1Hz to 100Hz, we record emphatically numerical results of different test points when their frequency are controlled to be the same and numerical results of a same test point at different frequency. The recording data show that the results of BEM are inconsistent with Morse theory when the frequency is lower than 20Hz.Secondly, we introduce the finite element method (FEM) and compare the numerical results we get in FEM with that in BEM or under Morse theory in the range of 1Hz to 30Hz frequency. The data show that, at the same frequency, the results of FEM and BEM are basically the same while the numerical simulation results of FEM and Morse theory are inconsistent if the frequency is less than 20Hz.Finally, this thesis divides the sound source item of the wave equation into the direct radiation source and the standing wave sound source after analyzing of sound source function and Fourier series which is based on physics and mathematics with the consideration of the influence of the direct sound in room acoustic field. Next we try to solve the corresponding segmented results with a revised Morse formula and then compare that with the results in BEM in order to construct an error image. It turns out that, at frequencies of 0 to 20Hz, the results solved from the revised Morse formula are more practical and the numerical simulation results are basically consistent with the BEM.