Aspects of a damped surface wave in the Fourier diamond spaces. New Surface Wave Analysis Methods (S.W.A.M.). Loic Martinez, Jean Duclos and Alain Tlnel bboratoire d’Acoustique Ultrasonore et d’Electronique, L.A. U.E., U.P. R. E.S.A. C.N.R,S. 6068 F Place Robert Schumn, BP 4006, 76610 Le Havre cedex, France. Abstract: The propagation of a damped surface wave is studied in a monodimentional medium using the Fourier diamond spaces. New properties are found for the wave number-frequency Ksi representation of the wave, In particular a link is established between the space and time charatetistics of the wave. me proposed Surface Wave Analysis Method (S.W.A.M,) is based on those properties. Using S.W.A.M. on a cylindrical shell, the A-wave is experimentally fully characterized. The agreement with theoretical results is excellent. SURFACE WAVES ANALYSIS METHODS (S.W.A.M.) First introduced by Bonnet [1,2], the four Fourier diamond spaces yield powerful wave representations. The representations S(X, t), S(x, o), Ksi(k, o), N(k, t) of a wave are performed using the the Fourier diamond @igure 1). S(x, t) S(X9 Fl~re 1. Fourier diamond spaces. N&t) In the present paper, ne-w properties are found mod;ling the propagation of a damped surface wave generated by a pulse. Such a surface wave is characterized by its complex wave number K(m)= K(m)+jK’’(m). The propagation of this wave (in a monodimentional medium of x axis) is defined by its space frequency representation S(x,w): S(x, o)= 5-1(x) eJK(~)x with 5-1(x) = 1 if x >0 and O elsewhere. Using Prony method in x direction, the complex K can be identified on short distances (Spatial-S. W.A.M. [3,4]). The wave number frequency representation Ksi(k, O) is the spatial Fourier transform of S(x, 0): Ksi(k, m)= 1 K“+j(k - K ) A cut of lKsil versus k is a Breit-Wigner function. Using a Taylor developpement of K(w), it can be shown that a cut of lKsil versus w is also a Breit-Wigner function if the surface wave is not too much attenuated. Such a cut has a modulus maximum for ~~: Ksi(k, O)= 1 ~’-j(o -Q) where 0’= K’(dw/dK) In simple way a new connexion is done between the space K and time -–W+jQ” aspects of a surface wave. Up to now this link was only established near the frequency resonances of a shell [5]. It is also shown that the representation Ksi allows us the identification of complex K (resp. complex Q) using k-A. R.M.A. modeling (resp. m- A. R.M.A. modeling). When the approximation is available, the wave number-time representation N(k, t) can be established: N(k, t)= ~-i(t) (d@/dk)eJQt The complex Q can be identified on small time interval using Prony method (Time-S.W.A.M. [3,4]). The dual space and time aspects of a surface wave is now illustrated by the experimental study of A-wave propagation on a cylindrical shell. 1359