Statics and Dynamics of the Thin Elastic Rod

2005 ◽  
pp. 121-148
Keyword(s):  
Elastic Rod ◽  
Statics And Dynamics ◽  
Thin Elastic Rod

Cantilever Rod in Cross Wind

1989 ◽  
Vol 56 (3) ◽  
pp. 639-643 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Numerical Integration ◽  
Large Deformation ◽  
Aerodynamic Drag ◽  
Flexural Rigidity ◽  
Relative Importance ◽  
Elastic Rod ◽  
Nondimensional Parameter ◽  
Cantilever Rod ◽  
Thin Elastic Rod

A thin elastic rod is held at one end in a strong cross wind. The nonlinear large deformation equations are formulated and solved by perturbation and numerical integration. The problem is governed by a nondimensional parameter K representing the relative importance of aerodynamic drag to flexural rigidity. For large K, phenomena such as nonuniqueness, instability, and hysteresis may occur.

PHYSICAL REALIZATION OF THE JIMBO-MIWA THEORY OF THE MODIFIED KORTEWEG-DE VRIES EQUATION ON A THIN ELASTIC ROD: FERMIONIC THEORY

1995 ◽  
Vol 10 (22) ◽  
pp. 3091-3107 ◽  
Author(s):  
SHIGEKI MATSUTANI
Keyword(s):  
Dimensional Space ◽  
Mkdv Equation ◽  
Dirac Field ◽  
Elastic Rod ◽  
Bilinear Method ◽  
Physical Relation ◽  
De Vries ◽  
Lax Operator ◽  
Thin Elastic Rod ◽  
Hirota Bilinear

Recently we found that the Dirac operator on a thin elastic rod is identical with the Lax operator of the modified Korteweg-de Vries (MKdV) equation while the thin elastic rod is governed by the MKdV equation. In this article, we will show the physical relation between the Hirota bilinear method and the Dirac field in a thin rod on two-dimensional space, along the lines of the Jimbo-Miwa construction of the MKdV soliton.

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