Decomposition of Rods Deformations: Asymptotic Behavior of Nonlinear Elastic Rods

2011 ◽  
pp. 171-197
Author(s):  
Georges Griso
Keyword(s):  
Asymptotic Behavior ◽  
Elastic Rods ◽  
Nonlinear Elastic

scholarly journals Solitary waves on nonlinear elastic rods. II.

1987 ◽  
Vol 81 (6) ◽  
pp. 1718-1722 ◽  
Author(s):  
M. P. Soerensen ◽  
P. L. Christiansen ◽  
P. S. Lomdahl ◽  
O. Skovgaard
Keyword(s):  
Solitary Waves ◽  
Elastic Rods ◽  
Nonlinear Elastic

scholarly journals Solitary waves on nonlinear elastic rods. I

1984 ◽  
Vol 76 (3) ◽  
pp. 871-879 ◽  
Author(s):  
M. P. Soerensen ◽  
P. L. Christiansen ◽  
P. S. Lomdahl
Keyword(s):  
Solitary Waves ◽  
Elastic Rods ◽  
Nonlinear Elastic

scholarly journals An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods

2002 ◽  
Vol 2 (8) ◽  
pp. 407-435 ◽  
Author(s):  
Shinuk Kim ◽  
Kevin L. Kreider
Keyword(s):  
Inverse Problems ◽  
Scattering Problem ◽  
Elastic Rods ◽  
Elastic Rod ◽  
Scattering Problems ◽  
Mathematical Basis ◽  
Cross Sectional ◽  
Weakly Nonlinear ◽  
The Time Domain ◽  
Nonlinear Elastic

Elastic wave propagation in weakly nonlinear elastic rods is considered in the time domain. The method of wave splitting is employed to formulate a standard scattering problem, forming the mathematical basis for both direct and inverse problems. A quasi-linear version of the Wendroff scheme (FDTD) is used to solve the direct problem. To solve the inverse problem, an asymptotic expansion is used for the wave field; this linearizes the order equations, allowing the use of standard numerical techniques. Analysis and numerical results are presented for three model inverse problems: (i) recovery of the nonlinear parameter in the stress-strain relation for a homogeneous elastic rod, (ii) recovery of the cross-sectional area for a homogeneous elastic rod, (iii) recovery of the elastic modulus for an inhomogeneous elastic rod.

Asymptotic behavior for linear and nonlinear elastic waves in materials with memory

2008 ◽  
Vol 354 (35-39) ◽  
pp. 4126-4137 ◽  
Author(s):  
R. Kirova ◽  
V. Georgiev ◽  
B. Rubino ◽  
R. Sampalmieri ◽  
B. Yordanov
Keyword(s):  
Asymptotic Behavior ◽  
Elastic Waves ◽  
Materials With Memory ◽  
Linear And Nonlinear ◽  
Nonlinear Elastic ◽  
With Memory

Asymptotic Behavior of Eigenvalues for Finite, Inhomogeneous Elastic Rods

1972 ◽  
Vol 39 (2) ◽  
pp. 595-597 ◽  
Author(s):  
Adnan H. Nayfeh
Keyword(s):  
Asymptotic Behavior ◽  
Finite Length ◽  
Free Vibrations ◽  
Elastic Rods ◽  
Elastic Rod ◽  
Elastic Parameters ◽  
Asymptotic Expressions

Asymptotic expressions for the eigenvalues and the corresponding eigenfunctions for the free vibrations of an inhomogeneous elastic rod with a finite length are derived. The derivation is based on the assumption that the elastic parameters and their derivatives vary continuously along the rod. A method which consists of a perturbation about the solutions of the homogeneous cases is used.

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