Displacement-based finite element method for guided wave propagation problems: Application to poroelastic media

Poroelastic materials are used extensively in the Literature for sound absorption and attenuation. Guided wave propagation in these materials is therefore of considerable interest to researchers. In the present paper, a finite element method is presented for guided wave propagation in poroelastic media. For harmonic vibrations, the finite element method gives rise to a quadratic eigenvalue problem in the phase speed. Solution of the standard finite element procedure is shown to excite modes with spurious phase speeds. It is shown that the real and spurious modes can be identified using the penalty constraint approach. For this, one needs to compute the rate of change of phase speed with the penalty constraint constant alpha. An expression for computing this rate of change of phase speed has been derived. It is shown that in most cases the rate of change of phase speed needs to be evaluated only at alpha=0. The results apply to a pure fluid and also to poroelastic media. In the process, analytical expressions are also derived for wave propagation in poroelastic cylinders. The use of reduced order integration to eliminate spurious modes is also discussed in this paper. Dispersion curves for the phase speeds are presented for the first few breathing modes of a poroelastic cylinder. Finally, results are presented for the case of a rigid, Lined ducted system. (C) 1996 Acoustical Society of America.