PSI - Issue 5

Kumar Anubhav Tiwari et al. / Procedia Structural Integrity 5 (2017) 973–980 Kumar Anubhav Tiwari et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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where α (f) is the frequency depended attenuation coefficient that can be assumed to be close to zero for the isotropic and lossless medium, V Ph is the phase velocity which is the function of frequency f and plate thickness h . The excitation signal u E (t) is applied at the transmitting zone ( i.e. MFC in our case of consideration) and must be multiplied by the correction factor C F corresponding to the specific GW mode as explained in Fig. 2. The value of C F depends on the behaviour of the transducer and it is the value of amplitude factor A F (y) in the desired direction. The MFC operates in elongation mode and particle velocities of its upper and lower half remain in opposite phase (Fig.2 (a), Fig.2 (b)).The amplitude factor A F (y) is the ratio of y -coordinate of the point sources (y n ) to the half-length ( L/2 ) of the MFC as explained in Fig. 2(c) and Fig. 2(d). In order to calculate the C F for the particular mode, the component of A F needs to be calculated in the direction of the wave propagation as shown in Fig. 2(e).

Fig.2. Calculation of correction factor (C F ) to be multiplied in excitation signal in case of MFC-P1: showing MFC-P1 operating in elongation mode (upper and lower half portion has opposite particle velocities) (a), 3D shape of MFC due to particle displacement (b), variations in the amplitude factor A F (y) with normalised particle velocity (u) (c ) showing the coordinates of point source in order to calculate the A F (y) (d) and correction factor (C F ) (component of A F in the direction of wave propagation) for the S0 mode ( A F ∙ sin θ L,P,I ) and for the SH0 mode ( A F ∙ cos θ L,P,I ) (e). The out-of-plane dominating component for the A0 mode is not shown for which C F can be assumed to be 1. In the case of MFC-P1, the value of C F is ) sin( , , k n m F A   , ) cos( , , k n m F A   for the S0 and SH0 mode respectively and C F is 1 for the A0 mode as shown in Fig. 2(e). Now, the spectrum of received signal at k th receiving point will be expressed as follows:       N n M m k n m k n m F T E k R k d U f C H f d f U 1 1 , , , , , ) 1 . ( , ( ) ( , )  (7) k n m d , , 1 is the distance diffraction factor described in Morin (2010), U E (f) is the spectrum of the excitation signal u E (t) which is calculated by FFT [u E (t)], U R,k ( f , θ k ) is the spectrum of the received signal, θ k is the angle in degree for the k th receiving point. where

The received signal in the time domain can be calculated by taking the inverse FFT.