Propagation of One-Dimensional Waves in Inhomogeneous Elastic Media

SIAM Review ◽  
1967 ◽  
Vol 9 (4) ◽  
pp. 671-679 ◽  
Author(s):  
Henry F. Cooper, Jr.
Keyword(s):  
Elastic Media ◽  
One Dimensional ◽  
Inhomogeneous Elastic Media

One-Dimensional Impact Waves in Inhomogeneous Elastic Media

1969 ◽  
Vol 36 (4) ◽  
pp. 803-808 ◽  
Author(s):  
Edward L. Reiss
Keyword(s):  
Asymptotic Methods ◽  
Variable Coefficients ◽  
Elastic Media ◽  
One Dimensional ◽  
Klein Gordon ◽  
Inhomogeneous Elastic Media ◽  
Impact Problems ◽  
Impact Data ◽  
The Impact ◽  
Impact Problem

Several one-dimensional impact problems for inhomogeneous elastic media are reduced by suitable transformations of variables to three different canonical forms. One of them is the impact problem for the wave equation with variable sound speed. Another, which we call Problem I, is the impact problem for the Klein-Gordon equation with variable coefficients. Several methods of approximating the solution of Problem I are discussed. The wave front approximation is obtained by assuming that sufficiently near the discontinuity propagating from the impacted boundary the solution has a Taylor series in time. The coefficients in the series are the time derivatives of the solution evaluated on the discontinuity. They are obtained from an analysis of the propagation of the discontinuity using the theory of weak solutions. A formal asymptotic expansion of the solution is obtained for oscillatory impact data. Reflections from boundaries are also considered. Perturbation methods for media with slowly varying inhomogeneities and asymptotic methods for media with rapidly varying inhomogeneities are briefly discussed.

Recursive Dispersion Relations in One-Dimensional Periodic Elastic Media

2008 ◽  
Vol 69 (3) ◽  
pp. 670-689 ◽  
Author(s):  
Ani P. Velo ◽  
George A. Gazonas ◽  
Erwin Bruder ◽  
Nancy Rodriguez
Keyword(s):  
Dispersion Relations ◽  
Elastic Media ◽  
One Dimensional

scholarly journals Anisotropic behaviour and elastic moduli of average isotropic and anisotropic elastic media

2019 ◽  
Vol 1 (3) ◽  
Author(s):  
Sadriten Tleukenov
Keyword(s):  
Elastic Moduli ◽  
Periodic Structures ◽  
Elastic Media ◽  
One Dimensional ◽  
Anisotropic Behaviour ◽  
Anisotropic Elastic

Using matricant method elastic moduli of occasionally heterogeneous isotropic and anisotropic elastic media were received. Anisotropic behaviour and conditions for change in anisotropy of media associated with averaging of one-dimensional periodic structures was determined. 

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