Energy flow analysis of poroelastic media

Abstract

• Heat-conduction type 1D energy models are developed for isotropic poroelastic media. • A notion of equivalent longitudinal bulk modulus and density of poroelastic media is introduced. • Criteria for the evaluation of energy models are provided in terms of the intrinsic parameters of the materials. • Developed models are validated by comparing with Biot's model at high frequencies. Energy flow analysis (EFA) has been used to formulate heat conduction-type energy models, which are effective in predicting high-frequency vibrational responses of structures. In this paper, energy models for poroelastic media are presented within the EFA framework. A one-dimensional case in which two dilatational waves propagate is considered. The derivation procedures rely on the notion of the equivalent longitudinal bulk modulus and density, which are defined based on the elastic and inertial coefficients of the frame and interstitial fluid and the relative wave motion between them. These parameters have roles similar to those of the equivalent bulk modulus and density of the fluid models for rigid- and limp-frame porous material and are used to represent the energy behavior of each propagating mode in terms of volume-averaged quantities. The resulting energy equations describe the propagation of the energy-related quantities of the two waves, and their capabilities are illustrated in cases in which a poroelastic layer is used to fill the cavity between two panels. The predicted results of energy models show a good approximation of the exact energy distributions of each wave, obtained from Biot's displacement formulation at high frequencies.