Derivation of the state matrix for dynamic analysis of linear homogeneous media

Abstract

A method to obtain the state matrix of an arbitrary linear homogeneous medium excited by a plane wave is proposed. The approach is based on projections on the eigenspace of the governing equations matrix. It is an alternative to manually obtaining a linearly independent set of equations by combining the governing equations. The resulting matrix has been validated against previously published derivations for an anisotropic poroelastic medium.<p>QC 20161014</p

A computational approach based on extended finite element method for thin porous layers in acoustic problems

“…It is seen that the dimension of transfer matrices is decided by the nature of the media, while the coefficients and their values in transfer matrices $$$ \left[{\mathbf{T}}^{\mathbf{f}}\right] $$$ and $$$ \left[{\mathbf{T}}^{\mathbf{P}}\right] $$$ depend on the specific material model. In this article, the JCA model, 34,35 one variant of the Limp model, see Reference 37 and a Biot matrix representation 42 are considered. We specify and discuss the coefficients in these models in Section 4.…”

Dynamic equations of a transversely isotropic, highly porous, fibrous material including oscillatory heat transfer effects

“…Only a subset of the field amplitudes representing the poroelastic medium are needed in the solution of the problem. 12 This is due to a linear dependence which is partially originating from the spatial dependence prescribed by the wavenumbers k x , k y , as well as being required to establish the coupling relations at the…”

“…To solve the dynamic equations including viscous dissipation and heat transfer, proposed here, a previously published Transfer Matrix Method (TMM) is employed. 11,12 This particular solution approach, which is based on a state space representation, is completely general in terms of the material symmetry as well as oblique incidence. The method will be briefly reviewed, and the proposed micro-structural modelling approach will be used to solve problems using only as input parameters the geometrical and the constitutive material parameters, and fibre microstructure parameters only.…”