Wave Propagation in Orthotropic Elastic Shells: Theoretical and Numerical Modeling

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

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.

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 simple model is proposed to study wave propagation in hard sphere-reinforced elastic random composites. Compared to existing related models, the proposed model is featured by a modified form of classical elastodynamic equations in which the inertia term is substituted by the acceleration field of the mass centre of a representative unit cell, supplied with a derived simple differential relation between the displacement field of the composite and the displacement field of the mass centre of a representative unit cell. The present model enjoys conceptual and mathematical simplicity although it is restricted to hard sphere-filled elastic composites in which the elastic moduli of embedded spheres are much (at least 4-5 times) stiffer than those of a softer matrix. Explicit formulas are derived for the attenuation coefficient and the effective phase velocity of plane longitudinal P-waves and transverse S-waves. The efficiency and reasonable accuracy of the present model are demonstrated by reasonably good agreement between the predicted results and some established known data. The proposed model could offer a potential general method to study various three-dimensional dynamic problems of hard sphere-filled elastic random composites.

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.

Accelerating numerical modeling of wave propagation through 2-D anisotropic materials using OpenCL

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.

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

Numerical modeling of wave propagation into a harbor using improved characteristic scheme

In this study, a combination of two fundamental frequencies f1=485 KHz and f2 = 515 KHz. The source transducers are placed on the surface of the sand 25 cm above the bottom and 20 cm below the water surface in the tank of dimension 74 × 47 × 43.5 cm simulating a seabed with sand of maximum particle size of 5 mm. Burger's equation is the simplest model for describing the second order nonlinear effects in the propagation of high amplitude plane waves and, in addition, the dissipative effects in media. Typically, the interactions of two acoustic waves at a discontinuity in a dispersive but homogeneous medium will generate harmonics and intermodulation terms. This is numerically modeled in Matlab using the finite difference time domain method with Neumann boundary conditions and practically verified with measurements from the tank. The measured and simulated results have shown significant agreement with the theory. For instance, second order intermod term show 2 dB decreases in amplitude for 7 mm increase in thickness at constant density of plywood. Also if the thickness is kept same, e.g., 5 mm, there is 10 dB drop in same intermod term for change in density from plywood 550 kg/m3 to copper 8930 kg/m3.

Experimental bistatic scattering measurements were made on two fluid-loaded, cylindrical shells in the frequency range of 2<ka<10. Data were collected for an empty shell and a duplicate shell stiffened with unequally spaced ring stiffeners and resiliently mounted wave-bearing internal structural elements. The shells were ensonified by wideband pulses of spatially plane waves at various angles of incidence. The scattered field was measured by a synthetic array in the transition and far-field regimes. Time domain focusing techniques are used to determine the transient dynamic structural response of the shell surface. Radon transforms are then used to identify and isolate individual wave events on the shell surface, such as the reflected and transmitted waves at a single ring stiffener. The results of these computations show that the internal structures greatly affect the dynamic response of the shell at these frequencies where the wavelengths are comparable to the lengths of the discontinuities in the shell. This research focuses on the effects of the ring stiffeners on the shear and compressional membrane waves in the shell. [The authors acknowledge NRL for acquisition of scattering data. Research supported by ONR.]

Wave propagation in shells of revolution having non-uniform geometries

2DH numerical model of nonlinear wave propagation based on a hybrid finite-volume and finite-difference scheme