Theoretical study of nonlinear elastic wave propagation

1994 ◽  
Vol 99 (B2) ◽  
pp. 2591-2600 ◽  
Author(s):  
K. R. McCall
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Theoretical Study ◽  
Elastic Wave Propagation ◽  
Nonlinear Elastic ◽  
Nonlinear Elastic Wave

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.

scholarly journals Theoretical Study of Memristor and \\ Time Reversal based\\ Nonlinear Elastic Wave Spectroscopy

2018 ◽  
Author(s):  
Sadataka Furui ◽  
Serge Dos Santos
Keyword(s):  
Elastic Wave ◽  
Time Reversal ◽  
Theoretical Study ◽  
Chaotic Oscillation ◽  
Acoustic Tomography ◽  
Linear Elastic ◽  
Strong Signal ◽  
Nonlinear Elastic ◽  
Nonlinear Elastic Wave ◽  
Elastic Unit

Principle of memristor presented by Leon Chua and time reversal based non-linear elastic wave spectroscopy (TR-NEWS) which can be applied to acoustic tomography are reviewed. Correlation of acoustic or electromagnetic nonlinear waves and its time reversed wave can produce strong signal. Materials like transducer or biological skin can be assumed to be composed of a large number of small elastic unit: hysteretic elementary unit (HEU), and one can take a HEU as a memristor whose operation depends on time. Relation between TR-NEWS and solitonic wave in fluid, and relation between decomposition of time reversal operator (DORT) and chaotic oscillation are discussed.

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