Space-time-wave number-frequency Z( x, t, k, f) analysis of SAW generation on fluid filled cylindrical shells

Abstract

A new 4D space-time-wave number-frequency representation Z( x, t, k, f) is introduced. The Z( x, t, k, f) representation is used for processing 2D space-time signal collection issued from wave propagation along a 1D medium. This representation is an extension along the time dimension of the space-wave number-frequency representation. The Z( x, t, k, f) representation is obtained by short time-space 2D Fourier transforming the space-time collection. The Z( x, t, k, f) representation allows the characterization transient aspects of wave generation and propagation in both space and time dimensions. The Z( x, t, k, f) representation is used to experimentally investigate Lamb wave generation and propagation around a cylindrical shell (relative thickness is equal to 0.03) surrounded by water and excited by a pulse (0.1 μs duration with 1–5 MHz transducers). Three kinds of fluids have been used inside the shell: air, water, propanol. In all the cases, the Z( x, t, k, f) analysis clearly identify the reflected field on the insonified side of the shell and it allows the measurement of the local reflection coefficients R( x, t, k, f). The generation and the propagation of Lamb waves are also quantified. For the liquid filled shells, the multiple internal reflections are revealed by Z( x, t, k, f) analysis: the local transmission coefficients T( x, t, k, f) are also measured. When local matching conditions allows Lamb wave generation, the multiple regeneration of Lamb wave is observed. Based on these results, a link is establish toward the theoretical results obtained by steady state approach and Sommerfeld–Watson transform.