A simple model for elastic wave propagation in hard sphere-filled random composites.

Wave propagation in glass fibre-reinforced polymer (GFRP) bars subjected to progressive damage—Experimental and numerical results

Shell type structures are used in a wide variety of industrial components, especially in automotive or aeronautic industries. A full understanding and predictive modeling of elastic waves propagation through those structures can be of great importance at their design stage for several reasons, such as the noise reduction in a vehicle or the control of high energy shock waves triggered by pyrotechnic cut in a space launcher. This paper deals with the theoretical and numerical modeling of elastic wave propagation in shells. The aim is to discuss the relevance of theoretical models and to develop appropriate and efficient numerical tools.

Seismic exploration of deep oil/gas reservoirs involves the propagation of seismic waves in high-pressure media. Traditional elastic wave equations are not suitable for describing such media. The theory of acoustoelasticity establishes the dynamic equation of wave propagating in prestressed media through constitutive relation using third-order elastic constants. Many studies have been carried out on numerical simulations for acoustoelastic waves, but are mainly limited to 2D cases. A standard staggered-grid (SSG) finite-difference (FD) approach and the perfectly matched layer (PML) absorbing boundary are combined to solve 3D first-order velocity-stress equations of acoustoelasticity to simulate wave propagating in 3D prestressed solid medium. Our numerical results are partially validated by plane-wave analytical solution through the comparison of calculated and theoretical P-/S-wave velocities as a function of confining prestress. We perform numerical simulations of acoustoelastic waves under confining, uniaxial and pure-shear prestressed conditions. The results show the stress-induced velocity anisotropy in acoustoelastic media, which is closely related to the direction of prestresses. Comparisons to seismic simulations based on the theory of elasticity illustrate the limitation of conventional elastic simulations for prestressed media. Numerical simulations prove the significant effect of prestressed conditions on seismic responses.

A theoretical model of elastic wave propagation in a cracked porous medium is developed in this paper. When elastic wave propagates through the cracked porous medium, the different physical properties and geometries in different pores structures lead to the fluid pressure gradient in cracks and between cracks and pores. The squirt-flow will take place in two mutually-perpendicular directions, thus, it has anisotropic characteristic. The wave respond contains the crack and background medium permeability information simultaneously. Owing to the fluid dynamic flow process, the effective elastic modulus is complex and frequency-dependent. When the wave frequencies are in high and low limit, the porous medium is elastic. The wave attenuation is obvious and the attenuation is frequency-dependent in the middle frequency region. The anisotropic permeability corresponding to anisotropic characteristic times in the cracked porous medium causes the wave propagation to be affected by the crack connectivity. There appears a second attenuation peak for larger thickness value of crack, meanwhile, and the peak of attenuation is influenced by the thickness value and radius of crack.

Continuous wave acoustic method for determination of moisture content in agricultural soil

On the generalized self-consistent model for elastic wave propagation in composite materials

In this study, we use the interferometric ghosts of the scattered surface waves for estimating the location of a near-surface scatterer. The scatterer is embedded in a homogeneous halfspace. We perform finite difference modeling of elastic wave propagation to calculate the seismograms. We choose different locations for virtual sources and obtain interferometric estimates of the scattered surface waves for these locations. We solve the inverse problem by using the interferometric traveltimes of the modeled scattered surface waves. The results show that the location of the scatterer is reasonably well estimated.

This paper is concerned with the numerical modeling of elastic wave propagation in layered media. It considers two isotropic homogeneous elastic solids in perfect contact. The interface is parallel to the free surface. Two finite difference methods are developed. The usefulness of the methods are investigated for long time simulations and the accuracy of the results are compared with the response from an approximate model.

Three‐dimensional (3D) elastic wave propagation modeling in the velocity‐stress formulation using finite differences (FDs) have been investigated for a homogeneous medium covered by a representative, relatively steep surface topography consisting of a 1D square root function. This scenario using various numerical implementations is explored. The behavior with regard to stability of long simulations is expected to be indicative of each numerical implementation's robustness for other types of topographies/media. Employing various combinations of the FD order was found only to change the time of the first incidence of instability. On the other hand, nonequidistant grids in the horizontal and vertical directions are found to be extremely useful for long‐term stability of 3D wave propagation modeling with our free‐surface boundary condition for single‐valued topographies. In particular dz ≥ (3/2) dx is found completely stable for all tested vP/vSratios. Such relationships of using dz > dx are also favorable for more accurate Rayleigh‐wave modeling. Setting the density equal to 1/10 of its interior value at one layer only at the surface is another simple means of achieving stability.

Compressional and shear-wave velocities from gas hydrate bearing sediments: Examples from the India and Cascadia margins as well as Arctic permafrost regions

A coupled three-dimensional fluid-elastic wave propagation mathematical model has been developed to handle environmental interactions in the ocean between a fluid medium and an elastic bottom. The existing model combines three-dimensional fluid and elastic wave propagation models with the incorporation of a set of horizontal fluid-elastic interface conditions. This paper extends the above model to consider an irregular fluid-elastic interface. The theoretical development of the irregular fluid-elastic interface equations is presented. Comparison of the fluid-elastic irregular interface to the horizontal case is one of the major objectives of this paper. Another major objective of this paper is the construction of a complete set of three-dimensional fluid-elastic wave equations, including the irregular interface, in a form suitable for stable numerical solution.

Laboratory measurements of P-wave and S-wave velocities across a surface analog of the continental crust–mantle boundary: Cabo Ortegal, Spain

Unidirectional fiber-reinforced composites continue to gain increasing importance in industrial applications particularly in the area of dynamic behavior. Many studies have focused on the determination of wave speed and attenuation of propagating waves in elastic fiber composites. These studies, however, most often use methods which are overly complicated and computationally expensive. Recently, a simple yet effective medium model was developed which provides explicit formulas for the dynamic behavior of P-waves, SV-waves and SH-waves. This model, however, failed to accurately predict the dynamic behavior of fiber-reinforced composites at higher frequencies around and beyond the bandgap region. In the present study, a refined analytical model is presented which supplements the aforementioned model with wave radiation damping. Our results show that the explicit formulas given by the present model are in good agreement with known numerical results in the literature for P-waves, SV-waves, and SH-waves.

On the modeling of wave propagation on non-uniform currents and depth

Wave propagation and thermal conduction properties can indicate structural damage to hot dry rock (HDR) caused by thermal shocks. Granite from the central paleo-uplift belt in the Daqing area in the northern Songliao Basin is the focus of this research. Wave propagation tests and thermal conduction tests were conducted on high-temperature specimens after natural cooling and water cooling. The influence of the cooling process with water on the apparent temperature and thermal shock velocity of rock masses is discussed. Changes in the P- and S-wave velocities, specific heat capacity, thermal diffusion coefficient, and thermal conductivity coefficient of specimens under different heat treatment conditions are analyzed and compared. The relationships between the wave propagation characteristics and the thermal conductivity values are established. The results indicate the following: (1) The apparent temperature and thermal shock velocity values of high-temperature rock masses show nonconstant rates of change from fast to slow. Rock masses with higher initial temperatures exhibit a continuous and strong thermal shock effect, and water temperature differences have only a limited effect on the thermal shock velocity over 20 s of cooling with water. (2) As the initial temperature increases or water temperature decreases, the P-wave velocity, S-wave velocity, thermal diffusion coefficient, and thermal conductivity coefficient values of high-temperature rock masses decrease overall, while the specific heat capacity values increase. The amplitude of change after water cooling is higher than that after natural cooling. When the initial temperature is below 100° C, the free water content is the main factor influencing the wave propagation characteristics and changes in the thermal conduction characteristics. When the initial temperature is greater than 300° C, the changes in both properties depend on the amount of thermal damage done to the rock mass. (3) The fitting results suggest that the wave propagation and thermal characteristics are closely related, and the damage factors are strongly consistent. The deviation of fitting coefficients is mainly due to the limited development of fractures in the small-sized specimens. The research results provide a reference for studies on thermal damage in HDR in the geothermal development process, and a method to determine the in situ thermal conductivity of reservoirs is proposed.