关键词: Laplace变换, 奇异性, 瞬态声场, 质点振速

Abstract: In the process of reconstructing the particle velocity in transient acoustic field, a singularity will be encountered at the zero frequency using the formula based on the fast Fourier transform (FFT). For solving the singularity, a method based on the Laplace transform for reconstructing the particle velocity in the transient acoustic field is proposed. In the proposed method, since the denominator of the reconstruction formula is a complex number whose real part is a non-zero constant, it doesn’t equal to zero at the zero frequency. So the singularity is solved fundamentally by the proposed method. With the circular piston in a rigid infinite baffle as the numerical simulation object, the above-mentioned two methods are respectively used to reconstruct the normal particle velocity on the surface of the piston. The reconstruction results demonstrate that when the ratio of the signal energy of particle velocity at zero frequency and the total signal energy is small, a satisfactory reconstruction result can be obtained by the method based on FFT. However, when the ratio is large, the larger reconstruction errors are produced by the method based on FFT, while since the method based on the Laplace transform can solve the singularity at the zero frequency, with this method a better reconstruction result can be obtained.

Key words: Laplace transform, Particle velocity, Singularity, Transient acoustic field