Propagation of elastic waves in a solid in the case of a nonlinear-elastic model of a continuous medium

1970 ◽  
Vol 6 (2) ◽  
pp. 140-144 ◽  
Author(s):  
G. N. Savin ◽  
A. A. Lukashev ◽  
E. M. Lysko ◽  
S. V. Veremeenko ◽  
S. M. Vozhevskaya
Keyword(s):  
Elastic Waves ◽  
Continuous Medium ◽  
Elastic Model ◽  
Nonlinear Elastic ◽  
Propagation Of Elastic Waves

Propagation of elastic waves in a solid for a four-constant elastic model of a continuous medium

1971 ◽  
Vol 7 (3) ◽  
pp. 260-263
Author(s):  
A. A. Lukashev ◽  
E. M. Lysko ◽  
S. V. Veremeenko ◽  
E. M. Vozhevskaya ◽  
V. F. Loshchinin
Keyword(s):  
Elastic Waves ◽  
Continuous Medium ◽  
Elastic Model ◽  
Propagation Of Elastic Waves

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.

scholarly journals Propagation of Elastic Waves in Prestressed Media

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Inder Singh ◽  
Dinesh Kumar Madan ◽  
Manish Gupta
Keyword(s):  
Elastic Waves ◽  
Plane Waves ◽  
Dynamical Equations ◽  
P Waves ◽  
General Solutions ◽  
External Forces ◽  
Propagation Of Elastic Waves

3D solutions of the dynamical equations in the presence of external forces are derived for a homogeneous, prestressed medium. 2D plane waves solutions are obtained from general solutions and show that there exist two types of plane waves, namely, quasi-P waves and quasi-SV waves. Expressions for slowness surfaces and apparent velocities for these waves are derived analytically as well as numerically and represented graphically.

Parametrization of the Propagation of Elastic Waves in a Medium with Ensembles of Disc-Shaped Inclusions

2018 ◽  
Vol 54 (1) ◽  
pp. 130-137 ◽  
Author(s):  
V. V. Mykhas’kiv ◽  
Ya. І. Kunets’ ◽  
V. V. Маtus ◽  
О. V. Burchak ◽  
О. К. Balalaev
Keyword(s):  
Elastic Waves ◽  
Propagation Of Elastic Waves

scholarly journals Analysis and approximation of a strain-limiting nonlinear elastic model

2014 ◽  
Vol 20 (1) ◽  
pp. 92-118 ◽  
Author(s):  
M Bulíček ◽  
J Málek ◽  
E Süli
Keyword(s):  
Elastic Model ◽  
Nonlinear Elastic
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