Theory of plane subsonic elastic waves in fluid-loaded anisotropic plates

Abstract

Propagation of plane elastic waves in plates of unrestricted anisotropy in contact with an arbitrary non–viscous compressible fluid is studied. A general formalism is worked out based on the method of plate impedance/admittance. It is applied to the subsonic velocity interval (below the sound speed in fluid) which encloses the modes localized along the plate faces and decaying into the fluid depth. The cases analysed include a plate immersed into fluid, a plate loaded by two different fluids, and a plate subjected to fluid loading on one side (in addition, the formal limiting cases involving an absolutely rigid wall are examined). For each of these settings, use of the plate–admittance analytical properties enables us to identify subsonic solutions of the real–valued dispersion equation in a transparent graphical fashion and thereby to reveal unambiguously the layout of the velocity branches. Possible types of the subsonic spectrum configuration are established, depending on the relation between the sound speed in the loading fluid(s) and certain reference velocities characterizing the plate. Evolution of the subsonic spectrum with changing the fluid/plate density ratio and with varying the difference between parameters of the fluids loading the plate from opposite sides is analysed. The conditions are discussed for some specific features, like the plate–fluid uncoupling, the intersection of branches and others. The particular case of plate faces lying in a symmetry plane is specified. The closed–form explicit solutions for the low–frequency onset of the velocity branches are derived for an arbitrary anisotropic plate and various types of fluid loading.