Numerical Model of the Spherical Elastic Wave Propagation in a Nonlinear Medium

1991 ◽  
Vol 02 (01) ◽  
pp. 250-253 ◽  
Author(s):  
IGOR BERESNEV
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Numerical Model ◽  
Elastic Wave ◽  
Nonlinear Medium ◽  
Nonlinear Effects ◽  
Seismic Wave Propagation ◽  
Geological Medium ◽  
Nonlinear Elastic ◽  
Nonlinear Elastic Wave

There are new experimental results showing that nonlinear effects are significant in seismic wave propagation through the upper part of the geological medium [1]. Nevertheless, no adequate models exist in seismology to describe theoretically such events. I describe here an attempt to derive a wave equation for the spherical nonlinear elastic wave and to solve it numerically.

Wave Motion of a Nonlinear Elastic Bar Subjected to Axial Excitation

2004 ◽  
Author(s):  
Liming Dai ◽  
Qiang Han
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Elastic Wave ◽  
Nonlinear Wave ◽  
Wave Motion ◽  
Initial Conditions ◽  
System Parameters ◽  
Elastic Bar ◽  
Nonlinear Elastic ◽  
Nonlinear Elastic Wave

This research intends to investigate the wave motion in a nonlinear elastic bar with large deflection subjected to an axial external exertion. A nonlinear elastic constitutive relation governs the material of the bar. General form of the nonlinear wave equations governing the wave motion in the bar is derived. With a modified complete approximate method, the asymptotic solution of solitary wave is developed for theoretical and numerical analyses of the wave motion. Various initial conditions and system parameters are considered for investigating the shape and propagation of the nonlinear elastic wave. With the governing equation of the wave motion of the bar and the solution developed, the characteristics of the nonlinear elastic wave of the bar are analyzed theoretically and numerically. Properties of the wave propagation and the effects of the system parameters of the bar and the influences of the initial conditions to the characteristics of the wave motion are investigated in details. Based on the theoretical analysis as well as the numerical simulations, it is found that the nonlinearity of the elastic bar may cause solitary wave in the bar. The velocity of the solitary wave propagating in the bar is related to the initial condition of the wave motion. This exhibits an obvious different characteristic between the nonlinear wave and that of the linear wave of an elastic bar. It is also found in the research that the solitary wave is a pulse wave with stable propagation. If the stability of the wave propagation is destroyed, the solitary wave will no longer exist. The results of the present research may provide guidelines for the wave motion analysis of nonlinear elastic solid elements.

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