The Wigner-Smith matrix in acoustic scattering: Application to fluid-loaded elastic plates

The Wigner-Smith matrix Q is built up by differentiation of the unitary condition of the scattering matrix S. The matrices Q and S both contain the same information but with different points of view. For structures with simple geometrical shapes such as plates or cavities, the acoustic scattering is a two channel scattering represented by a 2 X 2 S matrix. The elements of the Q matrix can be described: (i) by means of the phase derivatives of the elements of the matrix S, (ii) by means of the phase derivatives of the eigenvalues of the S matrix. The equivalence of these two descriptions allows one to express the phase derivatives of (i) in terms of the phase derivatives of (ii). The Wigner-Smith matrix concept enables one to unify and to improve both the phase gradient method and the eigenvalue method in the frame of the multichannel scattering. It obviously incorporates the resonance scattering theory. Approximate resonant formulas and numerical results are given for the case of fluid loaded elastic isotropic plates in order to check the validity of the method. (c) 2006 Acoustical Society of America.