Structural and acoustical wave interaction at a wedge-shaped junction of fluid-loaded plates

Abstract

Two semi-infinite elastic plates are joined along a line forming a wedge structure with unilateral fluid loading in the outer sector of the two plates. The structure is modeled using thin plate theory, allowing freely propagating flexural and longitudinal waves. The junction is mechanically connected with an applied force and moment acting there to simulate a possible internal connection. The general two-dimensional solution is described for incidence of time harmonic structural or acoustical waves. The total pressure is expressed as a Sommerfeld integral, the integrand comprising Malyuzhinets functions and particular solutions of certain difference equations. The junction conditions reduce to a system of four linear equations. Numerical examples indicate the coupling between the modes for welded steel plates in water. Acoustic plane-wave incidence on the flattest junction considered is converted almost equally, in terms of energy, among diffracted flexural and longitudinal waves. The coupling to flexural energy increases with the angle of the water wedge sector, at the expense of the longitudinal energy which vanishes in the limit as the water occupies the entire domain except for a strip comprising the two plates. An incident longitudinal wave generates relatively little acoustic sound for all wedge angles considered, with most of its energy redistributed among structural modes. The acoustical diffraction is generally greater for flexural incidence. Comparison with the dry structural diffraction coefficients indicates that the fluid loading effects for steel and water configurations can be significant for frequencies less than one-fifth of the coincidence frequency, but are small for higher frequencies.