A numerical study of wave propagation in poroelastic media by use of the localized differential quadrature (LDQ) method

Abstract

Some materials, such as cartilages and living bones, are made of an elastic matrix containing interconnected fluid-saturated pores. Their mechanical behaviors cannot be described by the theory of elasticity. The right theory for such materials is poroelasticity. Since many investigations on poroelasticity have been conducted on static problems, the study on wave propagation is of great importance. First in this thesis, the theory of wave propagation in fluid-saturated poroelastic media and the localized differential quadrature (LDQ) method are introduced. Using this LDQ method, the governing equations can be solved together with fourth-order Runge-Kutta method. Second, wave propagations in one-dimensional poroelastic media are investigated. The numerical results are compared with the closed-form analytical solutions, where a very good agreement is achieved. Finally, the problems of wave scattering in 2-D and 2-D holed poroelastic media are further investigated to get a thorough understanding of wave propagation, which simultaneously validate the LDQ method.