Abstract:
Two semi-infinite elastic plates are joined along a line forming a wedge structure with unilateral fluid loading in the sector of angle 2(Phi). 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 2-D solution is described for incidence of time harmonic structural or acoustical waves. The method of Osipov is used to express the total pressure as a Sommerfeld integral, the integrand comprising Malyuzhinets functions and particular solutions of certain difference equations. The junction conditions reduce to a system of eight linear equations. Numerical examples indicate the coupling between the modes for different wedge angles, specifically (Phi)=112.5(degrees), 135(degrees), and 157.5(degrees), for steel plates in water. Acoustic plane wave incidence on the flatter junction (112.5(degrees)) is converted almost equally, in terms of energy, among diffracted flexural and longitudinal waves. The coupling to flexural energy increases with the wedge angle, at the expense of the longitudinal energy which vanishes as (Phi)->180(degrees). An incident longitudinal wave generates relatively little acoustic sound for all values of (Phi) considered, with most of its energy redistributed among structural modes. The acoustical diffraction is generally greater for flexural incidence. [Work supported by ONR.]