Ultrasonic transient bounded-beam propagation in a solid cylinder waveguide embedded in a solid medium

Abstract

A semianalytical solution alternative and complementary to modal technique is presented to predict and interpret the ultrasonic pulsed-bounded-beam propagation in a solid cylinder embedded in a solid matrix. The spectral response to an inside axisymmetric velocity source of longitudinal and transversal cylindrical waves is derived from Debye series expansion of the embedded cylinder generalized cylindrical reflection/transmission coefficients. So, the transient guided wave response, synthesized by inverse double Fourier-Bessel transform, is expressed as a combination of the infinite medium contribution, longitudinal, transversal, and coupled longitudinal and transversal waveguide sidewall interactions. Simulated (f, 1/lambdaz) diagrams show the influence of the number of waveguide sidewall interactions to progressively recover dispersion curves. Besides, they show the embedding material filters specific signal portions by concentrating the propagating signal in regions where phase velocity is closer to phase velocity in steel. Then, simulated time waveforms using broadband high-frequency excitation show that signal leading portions exhibit a similar periodical pattern, for both free and embedded waveguides. Debye series-based interpretation shows that double longitudinal/transversal and transversal/longitudinal conversions govern the time waveform leading portion as well as the radiation attenuation in the surrounding cement grout. Finally, a methodology is deduced to minimize the radiation attenuation for the long-range inspection of embedded cylinders.