A computational method to calculate the longitudinal wave evolution caused by interfaces between isotropic media

Abstract

This paper presents a computational method to calculate the reflected and transmitted ultrasonic fields at interfaces of complex geometry. The method is performed in two steps. As first step, the velocity potential impulse response from an arbitrary aperture is determined at the interface using the Rayleigh integral and considering the reflection and transmission coefficients. In a second step, the simulated fields are calculated by applying the RayleighSommerfeld integral to the whole, extended interface. In order to validate the method, some experimental cases as, for instance, plane and cylindrical concave surfaces between two media (water-acrylic) were tested. The experimental ultrasonic fields are in good agreement with those provided by the model. Furthermore, in the work, the compromise between the accuracy of the method and the computation time is studied.

Acoustic beam modeling of ultrasonic transducers and arrays using the impulse response and the discrete representation methods

“…This method permits to calculate, in the time domain, the acoustic pressure induced in the medium by the transducer in an arbitrary spatial point. The method was initially proposed in acoustics by Stephanishen (Stephanishen, 1971) and, in order to obtain the exact solution of the impulse response, it is necessary to calculate complex integrals, only possible in the simplest geometry cases: circular pistons (Lockwood and Willette, 1973;Djelouah and Baboux, 1992), rectangular transducers (San Emeterio and Gómez-Ullate, 1992), triangular apertures (Jensen, 1996) and ring segments (Martínez et al, 2001).…”

“…The discrete method permits to analyze different transducer geometries (Jensen and Svendsen, 1992) and inherent problems of the acoustic beam generation (Piwakowski and Sbai, 1999). Moreover, the method can be used to investigate acoustic beams when transmission and reflection phenomena are involved (Buiochi et al, 2004;Belgroune et al, 2008).…”

Field modelling acceleration on ultrasonic systems using graphic hardware

“…These methods are based on the impulse response (IR) method [3][4][5][6][7][8][9][10], the angular spectrum technique [11][12][13], the finite element analysis [14,15], optical geometry studies [16,17], multi-Gaussian beam models [18] and so on. Using some of them, simulation tools have been developed for evaluation assessment in medical applications [19] or other sophisticated software packages, such as the CIVA program [20] for industrial NDE.…”

Impulse ultrasonic fields radiated by a linear transducer through a liquid-solid interface

“…Nevertheless, in the approximation of geometrical optics, a solution has been given. This one consists in refracting the hemispherical wave with the same transmission coefficient as the plane wave [8]- [9] or, by breaking up the incident field of spherical waves into an angular spectrum of plane waves via space Fourier transforms [10]. Beside to this work, other authors have studied the diffraction problem in the case of a plane interface, by the method of the angular spectrum by using the FFT.…”

“…The waves predicted by this model are compared with those obtained using angular spectrum method [11], and those obtained recently by using impulse response method [9], [12].…”