Error evaluation of the structural intensity measured with a scanning laser Doppler vibrometer and a k-space signal processing

In structural intensity measurements, the calculation error in the higher-order spatial derivatives contained in the derivation has a large effect on the measurement accuracy, since the derivative operations magnify the noise. To overcome the difficulty in calculating the derivatives, the authors employ the k-space processing which is based on the Fourier transform. Then, in this paper, a k-space filter is introduced to reduce the noise further. On the other hand, a noncontact method to measure the vibration distribution is necessary in order to avoid the loading effect on the specimen. An optical method is one of the most promising candidates for this purpose. This paper presents an error evaluation of the structural intensity as measured with a scanning laser Doppler vibrometer and the k-space signal processing. The effectiveness of the combination of the noncontact optical method and the k-space method is confirmed by both simulations and experiments. First, the error in calculating structural intensity is examined numerically using a one-dimensional beam model. As a result, it became clear that the cutoff wave number for k-space filtering should be one and a half of the wave number of the measured vibration to minimize the influence of the error in the measured data. Furthermore, basic measurement conditions such as the minimum number of data points and the sampling rate are studied for practical use of the k-space method. Lastly, the results of the numerical studies are confirmed by the experiments for a beam and a two-dimensional plate. (C) 1996 Acoustical Society of America.