The effective second‐order elastic constants of a strained crystal using the elastic wave propagation in a homogeneously deformed material

1988 ◽  
Vol 63 (12) ◽  
pp. 5728-5732 ◽  
Author(s):  
R. Ramji Rao ◽  
A. Padmaja
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Constants ◽  
Second Order ◽  
Elastic Wave Propagation ◽  
Strained Crystal

Compact second-order time-domain perfectly matched layer formulation for elastic wave propagation in two dimensions

2016 ◽  
Vol 22 (1) ◽  
pp. 20-37 ◽  
Author(s):  
Hisham Assi ◽  
Richard S. Cobbold
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Computational Cost ◽  
Perfectly Matched Layer ◽  
Two Dimensions ◽  
Second Order ◽  
Elastic Wave Propagation ◽  
Discrete Models ◽  
Computational Stability ◽  
Spatial Frequencies

A new second-order formulation is obtained for elastic wave propagation in 2D media bounded by a perfectly matched layer (PML). The formulation uses a complex coordinate stretching approach with a two-parameter stretch function. The final system, consisting of just two second-order displacement equations along with four auxiliary equations, is smaller than existing formulations, thereby simplifying the problem and reducing the computational cost. With the help of a plane-wave analysis, the stability of the continuous formulation is examined. It is shown that by increasing the scaling parameter in the stretch function, any existing instability is moved to higher spatial frequencies. Since discrete models cannot resolve frequencies beyond a certain limit, this can lead to significant computational stability improvements. Numerical results are shown to validate our formulation and to illustrate the improved stability that can be achieved with certain anisotropic media that have known issues.

Elastic wave‐propagation simulation in heterogeneous media by the spectral moments method

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1269-1281 ◽  
Author(s):  
Valérie Rousseau ◽  
Claude Benoit ◽  
Roger Bayer ◽  
Michel Cuer ◽  
Gérard Poussigue
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Continued Fraction ◽  
Heterogeneous Media ◽  
Finite Difference Methods ◽  
Second Order ◽  
Elastic Wave Propagation ◽  
Spectral Moments ◽  
Dynamic Matrix ◽  
Moments Method

The second‐order elastic wave propagation equations are solved using the spectral moments method. This numerical method, previously developed in condensed matter physics, allows the computation of Green’s functions for very large systems. The elastic wave equations are transformed in the Fourier domain for time derivatives, and the partial derivatives in space are computed by second‐order finite differencing. The dynamic matrix of the discretized system is built from the medium parameters and the boundary conditions. The Green’s function, calculated for a given source‐receiver couple, is developed as a continued fraction whose coefficients are related to the moments and calculated from the dynamic matrix. The continued fraction coefficients and the moments are computed using a very simple algorithm. We show that the precise estimation of the waveform for the successive waves arriving at the receiver depends on the number of moments used. For long recording times, more moments are needed for an accurate solution. Efficiency and accuracy of the method is illustrated by modeling wave propagation in 1-D acoustic and 2-D elastic media and by comparing the results obtained by the spectral moments method to analytical solutions and classical finite‐difference methods.

scholarly journals Active tuning of elastic wave propagation in a piezoelectric metamaterial beam

AIP Advances ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 065009
Author(s):  
Xi-Ning Zhao ◽  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Huayan Pu
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Wave Propagation

Elastic wave propagation in hierarchical lattices with convex and concave hexagons stacked vertexes

2019 ◽  
Vol 146 (3) ◽  
pp. 1519-1527 ◽  
Author(s):  
ZhiWei Zhu ◽  
ZiChen Deng ◽  
ShuZhan Tong ◽  
BenJie Ding ◽  
JianKe Du
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Wave Propagation ◽  
Hierarchical Lattices
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