Wavenumber Processing Techniques to Determine Structural Intensity and Its Divergence from Optical Measurements without Leakage Effects

Abstract

The technique of processing data in the wavenumber domain based on the Spatial Fourier Transform (SFT), is a powerful tool to compute higher-order partial derivatives occurred in the expressions of the structural intensity and its divergence. However, performing directly the SFT usually results in great distortions if a discontinuity occurs in spatial periodicity (leakage effect). The worst thing is that the divergence of a free plate cannot correctly be estimated by existing wavenumber processing such as the STF and zero padding method. In this paper, a new algorithm -- mirror processing, is developed. By the use of vibrating velocity measured from the technique of laser scanning vibrometry, the structural intensity, its divergence and the force distribution are evaluated by different techniques of wavenumber processing. It is shown that the distortions caused by leakage effects can be removed by using advanced algorithms.

Measurement of vibrational energy flow in a plate with high energy flow boundary crossing using electronic speckle pattern interferometry

“…This method is addressed in this work as the mirror-reverse-shear (MRS) periodisation technique. A second periodisation technique was proposed by Pascal et al [12]. This method will be addressed in this work as the mirror-processing (MP) technique.…”

“…The k-space derivation method is potentially more accurate than the finite difference approximation [1][2][3]. However a drawback of this method stems from the windowing effect due to Fourier transforming periodic signals consisting of a non-integer number of periods [12]. In this case spectral leakage will affect the accuracy of the resulting spectrum.…”

“…Inspection of Eq. (12) shows that the first term of Eq. (12) is equivalent to the net energy flow per unit length and, thus, the second term of Eq.…”

“…al. [10][11][12] applied holographic interferometry to measure structural intensity in a plate by measuring the out-of-plane velocity of the whole vibration field. For comparison reasons an energy transfer indicator was employed to compare measured intensity with the theoretical intensity present in an infinite plate due to flexural wave propagation.…”

Analytical modelling of flexural vibration of arbitrary flat plates by the boundary forming approach

“…A method developed by Pascal et al [33] provides a solution in stationary cases: the vibration field sampled by a scanning vibrometer is converted by Spatial Fourier Transform (SFT) into wavenumber space. In such a space, the displacement becomes an analytical function of spatial wavenumber, and thus the higher-order derivatives can be easily worked out.…”