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基于Laplace变换的瞬态声场质点振速重建方法 被引量:1

Method Based on the Laplace Transform for Reconstructing the Particle Velocity in the Transient Acoustic Field
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摘要 在瞬态声场质点振速的重建过程中,基于快速傅里叶变换(Fast Fourier transform,FFT)的重建公式在零频处存在奇异性,为此提出基于Laplace变换的瞬态声场质点振速重建方法。由于该方法重建公式中的分母为复数,而该复数的实部是一个不为零的常数,因此当频率为零时,分母并不为零,从而可从根本上解决零频处的奇异性问题。以固定在无限大障板上的圆形活塞为数值仿真对象,分别运用上述两种方法对活塞表面的法向质点振速进行重建。重建结果表明当质点振速信号在零频处的能量占信号总能量的比例较小时,运用基于FFT的方法进行重建可获得较满意的重建结果;但当质点振速信号在零频处的能量占信号总能量的比例较大时,运用基于FFT的方法进行重建会产生较大的重建误差,而由于基于Laplace变换的方法解决了零频处的奇异性问题,因此运用该方法进行重建可获得较好的重建结果。 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.
出处 《机械工程学报》 EI CAS CSCD 北大核心 2011年第19期68-73,共6页 Journal of Mechanical Engineering
基金 国家自然科学基金(10974040 11004045) 教育部新世纪优秀人才支持计划(NCET-08-0767) 高等学校博士学科点专项科研基金(20100111110007)资助项目
关键词 瞬态声场 质点振速 奇异性 LAPLACE变换 Transient acoustic field Particle velocity Singularity Laplace transform
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参考文献16

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