scholarly journals Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: the KdV, BBM, and CH equations

2015 ◽  
Vol 64 (3) ◽  
pp. 256 ◽  
Author(s):  
H A Erbay ◽  
S Erbay ◽  
A Erkip
Keyword(s):  
Elastic Medium ◽  
Wave Motion ◽  
Nonlinearly Elastic ◽  
Nonlinearly Elastic Medium

A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void

1986 ◽  
Vol 16 (2) ◽  
pp. 189-200 ◽  
Author(s):  
C. O. Horgan ◽  
R. Abeyaratne
Keyword(s):  
Elastic Medium ◽  
Bifurcation Problem ◽  
Nonlinearly Elastic ◽  
Nonlinearly Elastic Medium

Anharmonic Waves in a Mindlin–Herrmann Rod Immersed in a Nonlinearly Elastic Medium

2020 ◽  
Vol 55 (8) ◽  
pp. 1284-1297
Author(s):  
V. I. Erofeev ◽  
A. V. Leonteva
Keyword(s):  
Elastic Medium ◽  
Nonlinearly Elastic ◽  
Nonlinearly Elastic Medium

The propagation of compressive-shear perturbations in a nonlinearly elastic medium

1964 ◽  
Vol 28 (3) ◽  
pp. 706-713
Author(s):  
V.S. Antsiferov ◽  
Kh.A. Rakhmatulin
Keyword(s):  
Elastic Medium ◽  
Nonlinearly Elastic ◽  
Nonlinearly Elastic Medium

THE PRODUCTION OF ELASTIC WAVES BY EXPLOSION PRESSURES. I. THEORY AND EMPIRICAL FIELD OBSERVATIONS

Geophysics ◽  
1942 ◽  
Vol 7 (2) ◽  
pp. 144-154 ◽  
Author(s):  
Joseph A. Sharpe
Keyword(s):  
Elastic Medium ◽  
Elastic Waves ◽  
Qualitative Agreement ◽  
Spherical Cavity ◽  
Wave Motion ◽  
Arbitrary Form ◽  
Field Observations ◽  
Interior Surface ◽  
Shot Point ◽  
Empirical Field

A solution to the problem of the wave motion produced when a pressure of arbitrary form is applied to the interior surface of a spherical cavity in an ideally elastic medium is derived. This solution is shown to be in qualitative agreement with a number of field observations of the effect of shot‐point conditions on the characteristics of reflection seismograph recordings.

scholarly journals III. On the mathematical theory of sound

1859 ◽  
Vol 9 ◽  
pp. 590-591 ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Elastic Medium ◽  
Mathematical Theory ◽  
Wave Motion ◽  
Horizontal Tube ◽  
Equation Of Motion ◽  
General Function ◽  
Direct Integration ◽  
General Integral

The principal feature of this communication is the discovery of an integral of a certain class of differential equations. This class includes, as a particular case, the differential equation of motion when a disturbance is transmitted through a uniform elastic medium confined in a horizontal tube. If the equation dy / dt = F( dy / dx ) be differentiated with regard to t , it produces the equation d 2 y / dt 2 = {F' ( dy / dx )} 2 · d 2 y / dx 2 ; which, by means of the general function F', can be made to coincide with any proposed differential equation in which the ratio between d 2 y / dt 2 and d 2 y / dx 2 is dependent on dy / dx only. The integral obtained in this manner is that which arises from the elimination of ( a ) between the two following equations,— y = ax + F ( a ) · t + φ ( a ), 0 = x + F' ( a ) · t + φ ' ( a ). This integral, though not found by the direct integration of the differential equation, and though evidently not the general symbolical integral of it, is proved to be the general integral for wave-motion, from its affording the means of satisfying all the necessary equations of initial disturbance and wave-motion.

Discussions and Communications

Geophysics ◽  
1942 ◽  
Vol 7 (4) ◽  
pp. 419-419
Author(s):  
GEORGE R. LAMB
Keyword(s):  
Elastic Medium ◽  
Spherical Cavity ◽  
Wave Motion ◽  
Analytic Solution ◽  
Arbitrary Form ◽  
Interior Surface ◽  
Explosion Process ◽  
Wave Phenomena

To the Editor: In his paper in the April and July 1942 issues of GEOPHYSICS, Dr. Sharpe gives a very enlightening analytic solution to the problem of the wave motion generated in an elastic medium by application of a pressure of arbitrary form to the interior surface of a spherical cavity. It is very encouraging to find that deductions regarding the relation of the amplitude and frequency of the generated wave to the physicai characteristics of the medium agree so well with empirical operation. A thorough understanding of the explosion process and its accompanying wave phenomena is a prerequisite to the final refinement of the seismograph as a tool of Exploration Geophysics. It is to be hoped that Dr. Sharpe and his colleagues, as well as others, will continue the combined analytic and experimental attack.

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