PSI - Issue 16

Zinoviy Nazarchuk et al. / Procedia Structural Integrity 16 (2019) 11–18 Zinoviy Nazarchuk, Leonid Muravsky, Dozyslav Kuryliak / Structural Integrity Procedia 00 (2019) 000 – 000

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The characteristic equation for determine the spectrum is as det[ / kd d c     and c is the wave velocity. In order to determine the resonance regimes, we investigated the complex roots of this equation, which was considered on a Riemann surface as a function of the spectral parameter  with branching points on the real axis n    and (2 1) / 2 n     , 1, 2, ... n  In Fig. 2, we represent the dependence of real ( 1(2,3) Re 0   ) and imaginary ( 1(2,3) Im 0   ) parts of the roots on / p L d  (for the first three roots). The behaviour of the curves in this figure demonstrates the possibility of excitation of high-Q resonance transverse vibrations in the given structure. We have established that the imaginary part of the complex resonance frequency decreases with increase the parameter / p L d  . For the considered dynamical system, we have obtained an estimate for the lower bound of the ratio between the crack/delamination length and layer thickness for which one can diagnose it on the basis of the excitation of a resonance response. The obtained values can be used for choosing the optimal regime of sounding aimed at the detection of defects of fixed sizes as well as for determining the values of defect increment under loading by the shift of the resonance frequency. Subtractive synchronized ESPI technique is based on producing of speckle interferograms (SIs) during US harmonic excitation of composite panels with variable frequency. If the composite panel is excited, each subsurface defect became oscillate on its own resonant frequency if it coincides with the time variable frequency of US waves. The US excitation works in the frequency scanning mode, and all defects that have resonant frequencies in the range from 15 to 150 kHz and more starts to vibrate harmonically at its own resonant frequencies if the sweep frequency coincides with them. So, each subsurface defect that is oscillated on resonant frequency induces local oscillations of the surface area or the region of interest (ROI) placed directly above this defect. Thus, the ROI begins to oscillate with the same frequency. Extreme thickening of the panel within the ROI corresponds to the maximum amplitude of the harmonic wave, and the panel extreme thinning within the ROI corresponds to its minimum amplitude, as it is shown in Fig. 3. On the other hand, surface oscillations on this frequency are absent or very small outside the ROI. To produce a fringe pattern mapping a subsurface defect within the ROI, two sequences of speckle interferograms (SIs) are recorded during harmonic US excitation of the studied panel. Each SI from the first sequence is produced by accumulation of K elementary SIs registered by a digital camera during the frame time T at the time gap  for maximum amplitude of US wave within each oscillatory period T US (  < T US /2). Each SI from the second sequence is produced immediately after a previous SI from the first sequence by accumulation of K elementary a b ( )] 0 I A    , where 3. Subtractive synchronized ESPI technique

/ p L d  ); 1, 2, 3 are the numbers of roots.

Fig.2. Real (a) and imaginary (b) parts of complex roots of equation (8) (

a

b

c

Fig. 3. (a) initial state of a composite panel and ROI; (b) extreme panel thickening within the ROI at the maximum amplitude of US wave; (c) extreme panel thinning within the ROI at the minimum amplitude of US wave.