A discussion on high-frequency wave energy behavior in viscoelastic media

Abstract

A time-varying energy equation is proposed for general high-frequency elastoacoustic waves. Derivations are presented through a wave approach and transport theory. The assumption of uncorrelated waves is adopted in the wave approach and leads to a second-order partial differential equation. A similar process is also mathematically verified in the derivation by means of transport theory. Both derivations allow a simplified energy-based equation to be formulated. This simplified formulation can be of real interest in many engineering applications. Precisely, the recent mathematical results obtained for the high-frequency asymptotic of hyperbolic partial differential equations are used to ease the derivation. Some developments are introduced to extend the classic transport theory for bounded elastoacoustic systems with damping. It is shown that the behavior of high-frequency elastoacoustic energy, being diffusive or wavefront, depends on the correlation lengths of the inhomogeneities of media. The proposed energy equation is mathematically different from the equation applied in the conventional approaches, which are used extensively in recent study of time-varying energy in medium-and high-frequency domains, such as transient statistical energy analysis (SEA) or the time-varying conductivity approach.