GEOMETRICAL-ACOUSTICS CONSIDERATION OF THE FLEXURAL MODES IN IMMERSED ANISOTROPIC WEDGES

Geometrical-acoustics approach interprets vibration modes localized at the edge of wedges as the quasi-plane flexural waves propagating in a plate of variable thickness. This approach is combined with the dispersion relation for flexural wave in a thin anisotropic fluid-loaded plate to analytically determine the subsonic velocities c of the localized modes in anisotropic immersed wedges. The transcendent equation in c is established for an arbitrarily anisotropic wedge material and a general case of the wedge–fluid coupling. An approximate explicit solution for c is obtained in the cases when the parameter of the wedge-fluid coupling θn/r is either small or large (here θ is the apex angle, n is the modal order, and r is the ratio of the fluid density and the wedge density). In both cases, the ratio of the wedge-mode velocities c/c0in the immersed and free wedge is a corresponding function of the coupling parameter θn/r. Provided that the wedge–fluid coupling is sufficiently pronounced, the ratio c/c0in the presence of anisotropy acquires the scaling factor, which depends appropriately on elastic coefficients of the wedge and turns to unity in the isotropic limit.