MODE STRUCTURE FOR FLUID–SOLID MEDIA AS DERIVED BY LOW-FREQUENCY ASYMPTOTICS

The modes in a laterally homogeneous fluid–solid medium can be classified according to their low-frequency behaviour. For each mode, the horizontal wavenumber k(ω) will tend to a complex limit q (possibly infinite, but that appears to be exceptional) as the angular frequency ω tends to zero. The modes with vanishing wavenumber limits q can be listed explicitly, they are finite in number for each particular medium. The non-zero finite limits q appear as the zeros of certain entire analytic functions, one particular function for each fluid or solid region in the medium (and also for each Riemann sheet in the presence of homogeneous half-spaces). The resulting low-frequency mode structure can be uncovered for each fluid–solid medium by computing the wavenumber limits q as provided by the different regions. Efficient and reliable numerical techniques for this purpose are proposed for homogeneously layered media, based on compound-matrix factorization. The mode structure can be carried to higher frequencies by tracking dispersion curves. The behaviour at double roots and branch points needs special consideration. Two examples are studied in detail, one from plate acoustics and one from underwater acoustics.