The paper presents the improved element-free Galerkin (IEFG) method for three-dimensional wave propagation. The improved moving least-squares (IMLS) approximation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares (MLS) approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a discretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scaling parameter, number of nodes and the time step length are considered for the convergence study.

The improved element-free Galerkin method for three-dimensional wave equation

Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity

Propagation of a Love wave in an initially stressed fluid-saturated anisotropic porous layer with an irregular boundary sandwiched between two isotropic half-spaces has been studied. The irregularity is assumed to be rectangular, and the perturbation method is used to obtain the displacement field in the porous layer. Finally, the dispersion relation for the assumed model is obtained, and the result is compared with those derived for the flat layer theory. The effect of porosity, initial stress, and irregularity of the porous layer in phase velocity is studied and shown graphically.

Dispersion of Love Wave Propagating in Irregular Anisotropic Porous Stratum under Initial Stress

The influence of boundaries on sound insulation of the multilayered aerospace poroelastic composite structure

Analytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E′) and shear modulus (G′) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, ν and ν′ remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain–displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, VP, VSV, and VSH, and the wave vectors, , and , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E′, G′/E′, and ν/ν′); and (3) the phase angle, θ. Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium. Copyright © 2009 John Wiley & Sons, Ltd.

Wave propagation in an inhomogeneous cross-anisotropic medium

Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties

Based on Biot's theory for transversely isotropic fluid saturated porous media, the complex dispersion equation for Love waves in a transversely isotropic fluid-saturated porous layered half-space is derived with the consideration of the inhomogeneity of the layer. The equation is solved by an iterative method. Detailed numerical calculation is presented for an inhomogeneous fluid-saturated porous layer overlying a purely elastic half-space. The dispersion and attenuation of Love waves are discussed. In addition, the upper and lower bounds of Love wave speed are also explored.

Propagation of Love Waves in an Inhomogeneous Fluid Saturated Porous Layered Half-Space with Properties Varying Exponentially

Time domain BEM analysis of dynamic response of a cylinder embedded in soil with frictional slip at the interface

A 2D time-domain Boundary Element Method (BEM) is applied to solve the problem of transient scattering of plane waves by an inclusion with a unilateral smooth contact interface. The incident wave is assumed strong enough so that localized separations take place along the interface. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (separation and contact regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of plane waves by the cross section of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed.

Zi-Mao Zhang

Papers

Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties

Propagation of Love Waves in an Inhomogeneous Fluid Saturated Porous Layered Half-Space with Properties Varying Exponentially

Time domain BEM analysis of dynamic response of a cylinder embedded in soil with frictional slip at the interface

Analysis of transient wave scattering from an inclusion with an unilateral smoothly contact interface by BEM