Transient ultrasonic field radiated by a circular transducer in a solid medium

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Abstract
The problem of the transient ultransonic field radiated by a thickness-mode transducer of circular shape in a solid medium is modeled by a homogeneous isotropic elastic half-space whose surface is subjected to a normal load uniformly distributed under the active area of the circular transducer. Taking account of these particular boundary conditions, the partial derivative equations that govern the propagation of elastic waves are solved using integral transform techniques. It is shown that the ultrasonic displacement at a field point can be expressed under the form of a convolution in time between the applied stress and a function defined as the impulse response for the displacement. The numerical simulations obtained using this formulation show that the radiated field is relatively complicated because of the diffraction by the transducer edges. The radiated field consists of a compression plane wave propagating in the geometric region straight ahead of the source, together with compression and shear edge waves emanating from the transducer circumference. Besides, the mode conversion of the compression edge wave that propagates along the radiating surface gives rise to conical head waves. For the experimental study, a wideband laser interferometer of Michelson type was used for the measurement of the ultrasonic displacements generated in steel specimens by a wideband circular transducer. The performances of the laser interferometer (wideband and point measurements) and the characteristics of the transducer and of its electrical excitation (radiation of ultrasonic pulses of very short duration) leads to results where all the field components are clearly separated in time. Besides, the validity of the theoretical model is checked quantitatively by comparing the experimental and simulated waveforms of the ultrasonic displacement.

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