A Theory of Viscoelastic Analogy for Wave Propagation Normal to the Layering of a Layered Medium

1979 ◽  
Vol 46 (2) ◽  
pp. 329-336 ◽  
Author(s):  
T. C. T. Ting ◽  
I. Mukunoki
Keyword(s):  
Wave Propagation ◽  
Viscoelastic Medium ◽  
Layered Medium ◽  
Present Theory ◽  
Ray Theory ◽  
Transient Waves ◽  
Linear Elastic ◽  
The Impact ◽  
Homogeneous Linear ◽  
Plane Wave Propagation

Plane wave propagation in the direction normal to the layering of a periodically layered medium is studied. A period consists of two layers of homogeneous, linear elastic or viscoelastic materials. A theory is presented in which the layered medium is replaced by an “equivalent” linear homogeneous viscoelastic medium such that the stress response in the latter and in the layered medium are identical at points which are the centers of the odd layers. A means for determining the relaxation function of this equivalent homogeneous viscoelastic medium is presented and the transient waves in the layered medium are obtained by solving the transient waves in the equivalent homogeneous viscoelastic medium. Stieltjes convolutions with “auxiliary” functions are used to determine the solutions at points other than the centers of the odd layers and at points in the even layers. Numerical examples are presented for an elastic layered medium and comparisions are made with solutions obtained by the ray theory. The results show that the present theory can predict satisfactorily the transient response at any point in the layered medium regardless of whether the point is near or far from the impact end.

Transient waves in a layered anisotropic elastic medium

1985 ◽  
Vol 397 (1812) ◽  
pp. 67-85 ◽  
Keyword(s):  
Wave Propagation ◽  
General Solution ◽  
Applied Load ◽  
Layered Medium ◽  
Elastic Materials ◽  
Transient Waves ◽  
Anisotropic Elastic Medium ◽  
Unit Step ◽  
Stress Components ◽  
Anisotropic Elastic

Wave propagation in a periodically layered medium is studied in which each period consists of two layers of homogeneous anisotropic elastic materials. The layered medium occupies the half-space x ≥ 0 in which the x -axis is normal to the layers. Transient waves in the layered medium are generated by a unit step load in time applied at x = 0. A general solution that applies to any x is obtained in the form of a Laplace transform. Asymptotic solutions valid for large x are then deduced. If the applied load at x = 0 is in the direction of one of the polarization vectors for the layered medium determined here, the stress components propagate uncoupled asymptotically. For general loadings, there are three ‘heads of the pulses’, each of which is in the form of an Airy integral.

Plane wave propagation in a rotating anisotropic medium with voids under the action of a uniform magnetic field

2016 ◽  
Vol 05 (03) ◽  
pp. 1650015
Author(s):  
Narottam Maity ◽  
S. P. Barik ◽  
P. K. Chaudhuri
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Plane Wave ◽  
Equations Of Motion ◽  
Magnetic Field Effect ◽  
General Nature ◽  
Linear Elastic ◽  
Paper Plane ◽  
Constant Magnitude ◽  
Plane Wave Propagation

In this paper, plane wave propagation in a rotating anisotropic material of general nature under the action of a magnetic field of constant magnitude has been investigated. The material is supposed to be porous in nature and contains voids. Following the concept of [Cowin S. C. and Nunziato, J. W. [1983] “Linear elastic materials with voids,” J. Elasticity 13, 125–147.] the governing equations of motion have been written in tensor notation taking account of rotation, magnetic field effect and presence of voids in the medium and the possibility of plane wave propagation has been examined. A number of particular cases have been derived from our general results to match with previously obtained results in this area. Effects of various parameters on the velocity of wave propagation have been presented graphically.

APPLICATION OF DYNAMIC PROGRAMMING TO THE PROBLEM OF PLANE WAVE PROPAGATION IN A LAYERED MEDIUM

Geophysics ◽  
1966 ◽  
Vol 31 (6) ◽  
pp. 1037-1048 ◽  
Author(s):  
E. K. Darby ◽  
Norman S. Neidell
Keyword(s):  
Dynamic Programming ◽  
Wave Propagation ◽  
Plane Wave ◽  
Layered Medium ◽  
Normal Incidence ◽  
Two Stage ◽  
Stage Process ◽  
Plane Wave Propagation ◽  
Recursive Relations ◽  
Layer Problem

The philosophy of dynamic programming is applied to the problem of plane wave propagation at normal incidence in a layered medium. Using the intuitive concepts of reflection, transmission, and delays, the problem is reduced to a two‐stage process or a two‐layer problem where one of the layers is inhomogeneous. A solution in terms of recursive relations is obtained and a method for compactly describing complex configurations of layers is given. The recursive relations proceed forward in time.

On the impact end in longitudinal dynamic plastic wave propagation

1978 ◽  
Vol 29 (1-4) ◽  
pp. 75-92 ◽  
Author(s):  
D. W. Nicholson ◽  
A. Phillips
Keyword(s):  
Wave Propagation ◽  
Plastic Wave ◽  
Longitudinal Dynamic ◽  
The Impact
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