Elastic waves in randomly stratified medium. Numerical calculations

1992 ◽  
Vol 92 (1-4) ◽  
pp. 143-163 ◽  
Author(s):  
Z. Kotulski
Keyword(s):  
Elastic Waves ◽  
Numerical Calculations ◽  
Stratified Medium

A Dispersive Homogenization Model Based on Lattice Approximation for the Prediction of Wave Motion in Laminates

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
G. Carta ◽  
M. Brun
Keyword(s):  
Elastic Waves ◽  
Wave Motion ◽  
Impact Excitation ◽  
Stratified Medium ◽  
Model Approximation ◽  
Wide Range ◽  
Lattice Approximation ◽  
Homogenization Model ◽  
Elastic Impedance ◽  
Propagation Of Elastic Waves

The propagation of elastic waves in a periodic laminate is considered. The stratified medium is modeled as a homogenized material where the stress depends on the strain and additional higher order strain gradient terms. The homogenization scheme is based on a lattice model approximation tuned on the dispersive properties of the real laminate. The long-wave asymptotic approximation of the model shows that, despite the simplicity of the parameters identification, the proposed approach agrees well with the exact solution in a wide range of elastic impedance contrasts, also in comparison with different approximations. The effect of increasing order of approximation is also investigated. A final example of a finite structure under an impact excitation proves that the model behaves well when applied in the transient regime and that it can be considered a simple but consistent approach to build efficient algorithms for the numerical analysis of elastodynamics problems.

PROPAGATION OF RADIO WAVES OVER A STRATIFIED GROUND

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 416-422 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Dielectric Constant ◽  
General Expression ◽  
Numerical Calculations ◽  
Stratified Medium ◽  
Radio Waves ◽  
Number Of Layers ◽  
Special Case ◽  
Wave Tilt

The propagation of vertically polarized radio waves over a horizontally stratified medium is investigated. A general expression for the “wave tilt” is derived for the case of any number of layers with arbitrary properties in each layer. Numerical calculations are carried out for the special case of only two layers which show that the conductivity and dielectric constant variations of the lower layers will affect the magnitude and phase of the wave tilt.

Absorbing boundary conditions for elastic waves

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 231-241 ◽  
Author(s):  
R. L. Higdon
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Wave Velocity ◽  
Elastic Waves ◽  
Numerical Models ◽  
Absorbing Boundary Conditions ◽  
P Wave ◽  
Stratified Medium ◽  
Computational Domain ◽  
Absorbing Boundary

Absorbing boundary conditions are needed for computing numerical models of wave motions in unbounded spatial domains. The boundary conditions developed here for elastic waves are generalizations of ones developed earlier for acoustic waves. These conditions are based on compositions of simple first‐order differential operators. The formulas can be applied without modification to problems in both two and three dimensions. The boundary conditions are stable for all values of the ratio of P‐wave velocity to S‐wave velocity, and they are effective near a free surface and in a horizontally stratified medium. The boundary conditions are approximated with simple finite‐difference equations that use values of the solution only along grid lines perpendicular to the boundary. This property facilitates implementation, especially near a free surface and at other corners of the computational domain.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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