This paper derives a complex dynamic modulus function for a poroelastic slab with finite length and uses this to examine the range of validity of quasi-static solutions to Biot's dynamic poroelasticity equations. It also examines the effects of side surfaces' boundary conditions on the solutions to the equations and presents systematic studies of the effects of the slab length to thickness ratio and of the dissipation terms on the slab's storage and loss moduli. Biot's equations of poroelasticity are first phrased in terms of solid and fluid displacements and then transformed into the Laplace domain. The Galerkin type finite element method is used to solve these equations. Using quadrilateral elements, the stiffness matrix for this method is then derived. The dynamic transfer functions are then obtained for the case of an impulsive displacement applied to the top surface of the slab. Cases of both permeable and impermeable side surfaces are considered. The resulting solutions for the Laplace transform of the impulsive excitation response are then transformed into frequency domain complex response functions, called complex dynamic modulus functions, which characterized the stiffness and damping of the slab. Parametric studies are then carried out employing the complex frequency response functions.
An Int. J. of computers and structures67(4), pp.267-277