Dynamic Analysis of Gradient Poroelastic Solids and Structures

Abstract

The present chapter presents a review of previous works of the authors on the subject of the dynamic analysis of gradient poroelastic solids and structures. First, the governing equations of motion of a fluid-saturated poroelastic medium with microstructural (for both the solid and fluid) and microinertia (for the solid) effects are derived. These equations are of an order of two degrees higher than in the classical case and consist of seven equations with seven unknowns in three-dimensions. Second, the propagation of plane harmonic waves in an infinitely extended medium is studied analytically for the low and high frequency range. This is accomplished by separating the equations of motion in their dilatational and rotational parts for which wave dispersion curves can be constructed. Third, a simple one-dimensional boundary value problem, that of the transient behavior of a gradient poroelastic soil column, is solved analytically/ numerically with the aid of numerical Laplace transform. Finally, on the basis of the above, conclusions are drawn and suggestions for future research are made.