scholarly journals Elastic Bending Energy: A Variational Approach

2017 ◽  
Vol 45 ◽  
pp. 1-45 ◽  
Author(s):  
Riccardo Capovilla ◽  
Keyword(s):  
Variational Approach ◽  
Bending Energy ◽  
Elastic Bending

Investigation of Parametric Resonance Instability in a Flexible Rod Slider Crank Mechanism

1991 ◽  
Author(s):  
David G. Beale ◽  
Shyr-Wen Lee
Keyword(s):  
Potential Energy ◽  
Parametric Resonance ◽  
Variational Approach ◽  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Bending Energy ◽  
Constrained Equations ◽  
Beam Bending ◽  
Floating Frame ◽  
Crank Mechanism

Abstract A direct variational approach with a floating frame is presented to derive the ordinary differential equations of motion of a flexible rod, constant crank speed slider crank mechanism. Potential energy terms contained in the derivation include beam bending energy and energy in foreshortening of the rod tip (which were selected because of the importance of these terms in a pinned-pinned rod parametric resonance). A symbolic manipulator code is used to reduce the constrained equations of motion to unconstrained nonlinear equations. A linearized version of these equations is used to explore parametric resonance stability-instability zones at low crank speeds and small deflections by a monodromy matrix technique.

Elastic magnetic curves of Ferromagnetic and superparamagnetic models on the surface

2020 ◽  
pp. 2150037
Author(s):  
Talat Korpinar ◽  
Ridvan Cem Demirkol ◽  
Vedat Asil
Keyword(s):  
Variational Approach ◽  
Bending Energy ◽  
Regular Surface ◽  
Energy Functionals ◽  
New Class ◽  
Darboux Vector ◽  
Critical Curves ◽  
Elastic Curves ◽  
New Energy ◽  
Approach Method

We are interested in defining new energy functionals and solving them by using the variational approach method and Darboux equations. That is, we aim to define a new class of elastic curves on the regular surface [Formula: see text]. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves on [Formula: see text]. As a result, we classify these critical curves as elastic magnetic curves of the Darboux vector family.

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