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

A new 4D space-time-wave number-frequency representation <f>Z(x,t,k,f)</f> is introduced. The <f>Z(x,t,k,f)</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 <f>Z(x,t,k,f)</f> representation is obtained by short time-space 2D Fourier transforming the space-time collection. The <f>Z(x,t,k,f)</f> representation allows the characterization transient aspects of wave generation and propagation in both space and time dimensions.The <f>Z(x,t,k,f)</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 <f>Z(x,t,k,f)</f> analysis clearly identify the reflected field on the insonified side of the shell and it allows the measurement of the local reflection coefficients <f>R(x,t,k,f)</f>. The generation and the propagation of Lamb waves are also quantified.For the liquid filled shells, the multiple internal reflections are revealed by <f>Z(x,t,k,f)</f> analysis: the local transmission coefficients <f>T(x,t,k,f)</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. [Copyright &y& Elsevier]