Small-Amplitude Wave Behavior in One-Dimensional Granular Solids

1977 ◽  
Vol 44 (4) ◽  
pp. 559-564 ◽  
Author(s):  
J. W. Nunziato ◽  
E. K. Walsh
Keyword(s):  
Wave Propagation ◽  
Shock Waves ◽  
Small Amplitude ◽  
Unbounded Domains ◽  
Uniqueness Of Solutions ◽  
Amplitude Wave ◽  
One Dimensional ◽  
Granular Solids ◽  
Linearized Theory ◽  
Progressive Waves

In this paper we consider the dynamic behavior of granular solids in the context of a one-dimensional, linearized theory. Uniqueness of solutions for unbounded domains is established and two wave propagation problems are solved. In particular, the dispersion relations for small-amplitude sinusoidal progressive waves are obtained and the evolution of small-amplitude shock waves is exhibited.

Thermoelastic Small-Amplitude Wave Propagation in Nonlinear Elastic Multilayers

2004 ◽  
Vol 9 (5) ◽  
pp. 555-568 ◽  
Author(s):  
Massimiliano Gei ◽  
Davide Bigoni ◽  
Giulia Franceschni
Keyword(s):  
Wave Propagation ◽  
Small Amplitude ◽  
Amplitude Wave ◽  
Nonlinear Elastic

Fracture of Lucite Cones by Shock Waves

1972 ◽  
Vol 39 (2) ◽  
pp. 390-394
Author(s):  
W. N. Sharpe
Keyword(s):  
Wave Propagation ◽  
Shock Waves ◽  
Tensile Stress ◽  
Fracture Criterion ◽  
Leading Edge ◽  
Propagation Theory ◽  
One Dimensional ◽  
Cone Axis ◽  
Cone Apex ◽  
Dimensional Wave

A compressive pulse applied to the base of a cone develops a tensile tail as it propagates toward the cone apex. This tension can cause fracture of the cone perpendicular to the cone axis before the leading edge of the pulse reaches the tip. It is shown that the elementary one-dimensional wave-propagation theory for cones and a time-independent critical tensile stress fracture criterion adequately describe the fracture of lucite cones subjected to narrow rectangular compressive pulses between 1 and 7 kilobars in magnitude.

Small Amplitude Wave Propagation in Hot Ionized Gases

1965 ◽  
Vol 8 (11) ◽  
pp. 2087 ◽  
Author(s):  
P. K. Khosla ◽  
M. P. Murgai
Keyword(s):  
Wave Propagation ◽  
Small Amplitude ◽  
Amplitude Wave

Shock waves and non-stationary flow in a duct of varying cross-section

1971 ◽  
Vol 46 (1) ◽  
pp. 111-128 ◽  
Author(s):  
Naruyoshi Asano
Keyword(s):  
Shock Waves ◽  
Cross Section ◽  
Small Amplitude ◽  
Stationary Flow ◽  
Shock Propagation ◽  
Sound Waves ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Propagation Law ◽  
Good Agreement

Sound waves of finite but small amplitude propagating into a quasi-steady, supersonic flow in a non-uniform duct are analyzed by means of a perturbation method. General properties of the flow and of the wave propagation are studied using a one-dimensional approximation. A shock propagation law in the unsteady flow is obtained. As an example, the formation and development of shock waves are discussed for a duct with a conical convergence. Comparisons of the theory with an experiment are also made; fairly good agreement is found.

Material stability, strong ellipticity and smoothness of equilibria

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Wave Propagation ◽  
Small Amplitude ◽  
A Priori ◽  
Strong Ellipticity ◽  
Amplitude Wave ◽  
Material Stability

Chapter 9 develops the notion of material stability on the basis of small-amplitude wave propagation. This is shown to correlate with the smoothness of finite equilibrium deformations, granted sufficient a priori regularity assumptions. The central role played by the condition of strong ellipticity is emphasized.

Wave propagation in a partilly-ionized chemically-reacting plasma

1973 ◽  
Vol 9 (3) ◽  
pp. 349-365 ◽  
Author(s):  
Ta-Ming Fang ◽  
Howard R. Baum†
Keyword(s):  
Wave Propagation ◽  
Chemical Reactions ◽  
Small Amplitude ◽  
Wave Motion ◽  
Dominant Role ◽  
Amplitude Wave ◽  
Longitudinal Waves ◽  
Long Wavelength ◽  
Chemically Reacting ◽  
Frozen Plasma

Multi-fluid equations derived in a previous paper are used to study small- amplitude wave motion in a partially ionized chemically-reacting plasma. The plasma is assumed to be infinite and without external fields. The dispersion equations are derived and solved both numerically and analytically for several limiting cases. The effects of chemical reactions have been explicitly obtained. It is found that at the long-wavelength limit, the ionization and recombination terms play the dominant role for the damping of certain longitudinal waves even for a nearly frozen plasma.

Small amplitude wave propagation in stratified media

1979 ◽  
Vol 29 (5) ◽  
pp. 487-494
Author(s):  
M. Khan ◽  
B. Chakraborty
Keyword(s):  
Wave Propagation ◽  
Small Amplitude ◽  
Stratified Media ◽  
Amplitude Wave
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