Energy velocity of elastic guided waves in immersed plates for complex frequencies and slownesses

Abstract

The computation of guided modes in fluid-loaded multilayer plates is generally done by a spatial approach, i.e. solutions are sought for a complex slowness. An alternative approach, less frequently employed, involves seeking solutions for complex frequencies. These frequencies correspond to plate resonances. They denote transient phenomena and the guided modes exhibit non-harmonic behavior. Consequently, conventional methods of averaging over time periods become unsuitable for calculating the means of energy quantities. In other words, the calculation of average fields cannot be reduced to a single average over a time period. To tackle this issue, for a predetermined mode, the average fields are obtained through a single averaging process applied to an arbitrary phase term. This averaging process renders independent the means of all energy quantities from the arbitrary origin phase. As usual, an additional integration across the thickness is conducted to derive total energy quantities. Doing this, the total average fields depend on both time and position on the surface plate. A set of four equations is derived from instantaneous and local energy balance equations. From these averages, the energy velocity can be directly calculated. The equations provide further insights into wave dispersion and damping along the energy flow direction, arising from viscoelastic losses and leakages in fluid.