Transient Fields Radiated by Nonuniform Trasnducers in a Solid Calculated by an Approximate Model and the Finite-Difference Method

Lhémery, Alain
Stacey, Richard
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Nonuniform broadband transducers have been shown to radiate transient fields of simpler time and space structures than conventional uniform transducers by modifying transducer diffraction effects [1, 2]. The echo-structure arising from a defect as measured in pulse-echo methods of NDT is a fortiori simplified since transducer diffraction effects occur both in radiation and in reception [2]. Most of the theoretical and experimental works on nonuniform transducers dealt with the propagation of pulses of ultrasound in fluids. In solids, the transient field radiated by even a simple compression wave disk-transducer directly coupled with an elastic half-space is very complex because diffraction effects leads to complex mode-conversion phenomena [3–5]. Such a transducer not only radiates a complex compression wave-field (comparable with that radiated in fluids by a similar transducer) but also a complex shear wavefield. In the present paper, three different source profiles are considered (same as in Ref. [2] where echo-responses from targets in fluids were studied): a conventional uniform profile, a nondiffracting profile and a profile reinforcing diffraction effects. The two nonuniform profiles are not ideal as those considered in [6]. We have developed industrial prototypes vibrating with these profiles (in [2], only laboratory-made transducers were considered). The present paper aims to show how they simplify the wavefield structure radiated in solids. To do this, both waveform and amplitude of the transient velocity radiated at various field-points are calculated by means of two methods: a recently proposed approximate solution [4] (improved in [5]) and a pure numerical scheme based on the finite-difference method [7]. First, the approximate solution is recalled [4, 5]. Analytic formulas for a uniform source profile are explicitly given. They are combined with the superposition principle to allow the computation of the field radiated by nonuniform but axisymmetrical source profiles considered herein. Then, the finite-difference scheme originally developed for NDT modeling [7] is briefly recalled. It allows the computation of the field radiated by arbitrary axisymmetrical source profiles. Both methods are used to predict the particle velocity radiated by the three profiles considered at various field-points either on- or off-axis and at different ranges. The accuracy of both methods is shown by comparing predicted waveforms. Finally, all the results are discussed to show advantages and disadvantages of using nonuniformly excited transducers in the context of pulse-echo methods of NDT.