Modeling of propagation and echo formation in a multilayered structure

Application of the ultrasonic pulse-echo technique for quality control of the multi-layered plastic materials

“…The main parameters of the model, such as ultrasound velocity, density, frequency-dependent attenuation and phase velocity dispersion in each layer are being iteratively changed until the global minimum min(F[c k , a k (f), v p,k (f), r k ]) of the target function F[c k , a k (f), v p,k (f), r k ], which has been expressed as a normalized root-mean-square error between the simulated and the experimental signals, is obtained. Here, c k , a k (f), v p,k (f), r k are sets of ultrasound velocities, attenuation, phase velocity dispersion and densities estimated for individual layers of the multi-layered object [11,12,14,15].…”

“…The multi-layered object may be simulated by a spatial pulse response, which consists of short spikes (denoted by delta Dirac functions) at different time instants t i , corresponding to reflections from the interfaces between adjacent layers with different acoustic properties [11,12,14,15]. Amplitudes A i of the reflected signals from the interfaces between adjacent layers in the spatial pulse response are given by hðt; x; y; zÞ ¼ P i ½A i dðt À t i Þ;…”

Ultrasonic oil-film thickness measurement: An angular spectrum approach to assess performance limits

“…Equation 13 is then multiplied by a phase term to account for propagation from plane 1 to plane 2 (i.e. the focal plane),…”

“…The adhesive joint was modelled using a spring model of the interface and showed good agreement with a number of normal and oblique incidence experiments. Croce et al [13] extended this analysis by using a full multi-layered system model.…”