scholarly journals Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations

Wave Motion ◽  
2015 ◽  
Vol 56 ◽  
pp. 221-238 ◽  
Author(s):  
Nicolas Favrie ◽  
Bruno Lombard ◽  
Cédric Payan
Keyword(s):  
Slow Dynamics ◽  
Longitudinal Vibrations ◽  
Elastic Bar ◽  
Nonlinear Elastic

Numerical Analysis for Acoustic Resonance of One-Dimensional Nonlinear Elastic Bar

2011 ◽  
Vol 50 (7) ◽  
pp. 07HB02 ◽  
Author(s):  
Ryuichi Tarumi ◽  
Tomohiro Matsuhisa ◽  
Yoji Shibutani
Keyword(s):  
Numerical Analysis ◽  
Acoustic Resonance ◽  
One Dimensional ◽  
Elastic Bar ◽  
Nonlinear Elastic

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.

Semi-Discrete Analytical Solution of Lumped Mass Finite Element Method for the Longitudinal Vibrations of an Elastic Bar

2013 ◽  
Vol 273 ◽  
pp. 234-239
Author(s):  
Jing Song Pan ◽  
Ji Chan Wang
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Analytical Solution ◽  
Longitudinal Vibration ◽  
Analytical Approximation ◽  
Longitudinal Vibrations ◽  
Lumped Mass ◽  
Elastic Bar ◽  
Element Method

The objective of this paper is to present semi-discrete analytical method for the longitudinal vibration of an elastic bar. Using lumped mass finite element method, we first obtain a system of second order ordinary differential equations. In terms of some transform technique we obtain the exact solution to the system, i.e. excellently semi-discrete analytical approximation to the longitudinal vibration. An example is given to illustrate the effectiveness of the proposed method.

On the Numerical Solution of One-Dimensional Continuum Problems Using the Theory of a Cosserat Point

1985 ◽  
Vol 52 (2) ◽  
pp. 373-378 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Numerical Solution ◽  
Body Force ◽  
Closed Form Solution ◽  
Form Solution ◽  
Element Approximation ◽  
One Dimensional ◽  
Linear Elastic ◽  
Elastic Bar ◽  
Cosserat Point ◽  
Nonlinear Elastic

The theory of a Cosserat point is specialized to describe the motion of a one-dimensional continuum. Attention is focused on two problems of an elastic bar. Vibration of a linear-elastic bar is considered in the first problem and static deformation of a nonlinear-elastic bar subjected to a uniform body force is considered in the second problem. A closed-form solution is derived for each problem by dividing the bar into two elements, each of which is modeled as a Cosserat point. The predictions of the two-element approximation are shown to be very accurate.

Numerical Analysis for Acoustic Resonance of One-Dimensional Nonlinear Elastic Bar

2011 ◽  
Vol 50 (7S) ◽  
pp. 07HB02
Author(s):  
Ryuichi Tarumi ◽  
Tomohiro Matsuhisa ◽  
Yoji Shibutani
Keyword(s):  
Numerical Analysis ◽  
Acoustic Resonance ◽  
One Dimensional ◽  
Elastic Bar ◽  
Nonlinear Elastic

scholarly journals A Finite-Volume Approach to 1D Nonlinear Elastic Waves: Application to Slow Dynamics

2018 ◽  
Vol 104 (4) ◽  
pp. 561-570 ◽  
Author(s):  
H. Berjamin ◽  
B. Lombard ◽  
G. Chiavassa ◽  
N. Favrie
Keyword(s):  
Finite Volume ◽  
Elastic Waves ◽  
Slow Dynamics ◽  
Finite Volume Approach ◽  
Nonlinear Elastic
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