Aspects of cylindrical shell resonances in the Fourier diamond spaces. Use of surface wave analysis methods (SWAM) on experimental or numerical datas

Abstract

For an attenuated surface wave (wave number K=K′+jK″), the resonant space-frequency S(x,ω) representation of a cylindrical shell is performed versus the angular position x. In this space, the MIIR properties are demonstrated. The resonant wave number-frequency representation Ksi(k,ω) is then obtained by spatial Fourier transform of S(x,ω). This two-dimensional second space clearly separates clockwise and anticlockwise propagating waves. The first ones are observed in the positive k values of Ksi, and the second ones in the negative k values of Ksi. The modulus of Ksi is maximum each time that the resonant condition is encountered [ω so that K′(ω) is integer]. As new results, the k cut of Ksi reveals the Sommerfeld Watson aspect of the problem and SWAM identify the complex K. On an ω cut of Ksi, SWAM identify the RST aspect of the target (and a little more): complex frequency resonances Ω=Ω′+jΩ″ for real modes n. SWAM is performed on experimental datas and on numerical form functions. The agreement with theoretical results obtained by RST is very good.

Transient space-time surface waves characterization using Gabor analysis

“…The 2D Fourier transform of s(x,t) can be used to quantify, a posteriori, the wave properties, like their attenuation and phase velocities [6][7][8][9][10][11][12][13]. With the help of Prony identification, the mixed representations S(x,ω) and N(kx,t) can be also used successfully [14][15]. However when the signal s(x,t) is a sum of identical wide band wave packets delayed in time and in space, identification based on S(x,ω) allows ones to precise where the waves are packets, not when, whether N(kx,t) allows the time localization, not the space one, and Ksi(kx,ky,ω) none of both as everything is accumulated.…”

“…For 3D data signals s(x,y,t), some of the 2D tools are still usable: S(x,y,ω) is useful for identifying the wave modes. However, the problem of wide band wave localization in both time and space encountered for the 2D case remains in the 3D case, and a second difficulty appears: identification by Prony like methods is not possible without a deeper prior knowledge of the experimental signal composition [14][15].…”