A CANONICAL PROBLEM FOR FLUID-SOLID INTERFACIAL WAVE COUPLING

Wave-coupling involving defects or obstacles on fluid-solid interfaces is of recurrent interest in geophysics, transducer devices, structura l acoustics, the acoustic microscope and related problems in non-destr uctive testing. Most theoretical analysis to date has, in effect, invo lved stress or pressure loadings along the interface, or scattering fr om surface inhomogeneities, that ultimately result in unmixed boundary value problems. A more complicated situation occurs if a displacement is prescribed over a region of the interface, and the rest of the int erface is unloaded (or stress/pressure loaded); the resulting boundary value problem is mixed. This occurs if a rigid strip lies along part of the interface and will introduce several complications due to the p resence of the edge. For simplicity a lubricated rigid strip is consid ered, i.e. it is smoothly bonded to the elastic substrate. To consider such mixed problems, e.g. the vibration of a finite rigid strip or di ffraction by a finite strip, a canonical semi-infinite problem must be solved. It is the aim of this paper to solve the canonical problem as sociated with the vibrating strip exactly, and extract the form of the near strip edge stress, and displacement fields, and the far-field di rectivities associated with the radiated waves. The near strip edge re sults are checked using an invariant integral based upon a pseudo-ener gy momentum tensor and gives a useful independent check upon this piec e of the analysis. The directivities will be useful in formulating a r ay theory approach to finite strip problems. An asymptotic analysis of the solution, in the far field, is performed using a steepest descent s approach and the far-field directivities are found explicitly. In th e light fluid limit a transition analysis is required to determine uni form asymptotic solutions in an intermediate region over which the lea ky Rayleigh wave will have an influence. In a similar manner to relate d work on the acoustic behaviour of fluid-loaded membranes and plates, there is beam formation in this intermediate region along critical ra ys.