Continua with microstructure: Cosserat theory

2010 ◽  
Vol 14 (8-9) ◽  
pp. 1011-1029 ◽  
Author(s):  
Euripides Papamichos
Keyword(s):  
Cosserat Theory ◽  
Continua With Microstructure

Mode Coupling-Type Instability of a Beam Subjected to Coulomb Friction

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yasuhiro Seo ◽  
Hiroshi Yabuno ◽  
Go Kono
Keyword(s):  
Mode Coupling ◽  
Coulomb Friction ◽  
Axial Direction ◽  
Laser Printer ◽  
Beam Model ◽  
Excitation Mechanism ◽  
Cosserat Theory ◽  
Floor Surface ◽  
Excited Oscillation ◽  
Mode Coupling Instability

To analyze the excitation mechanism of self-excited oscillation in a beam that is in contact with a moving floor surface such as a cleaning blade, which is a beam mounted in a laser printer to clean the photoreceptor, we study a beam subjected to Coulomb friction and theoretically predict the occurrence of self-excited oscillation through mode-coupling instability. We present an extensible beam model, and derive its governing nonlinear equations by means of special Cosserat theory, which allows for the extensibility of the beam to be considered. The boundary conditions on the end of the beam are unique because the end of the beam makes contact with the moving floor surface. We used a discretized linearized governing equation and performed linear stability analysis. The results indicate that self-excited oscillation in the beam is produced due to both Coulomb friction and mode coupling of the bending and extension of the beam based on the extensibility in the axial direction.

scholarly journals Solitary flexural–gravity waves in three dimensions

2018 ◽  
Vol 376 (2129) ◽  
pp. 20170345 ◽  
Author(s):  
Olga Trichtchenko ◽  
Emilian I. Părău ◽  
Jean-Marc Vanden-Broeck ◽  
Paul Milewski
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Cosserat Theory ◽  
Theme Issue ◽  
Flexural Gravity Waves ◽  
Forced Waves ◽  
Ice Phenomena

The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369 , 2942–2956 ( doi:10.1098/rsta.2011.0104 )). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

Dynamics modeling of a soft arm under the Cosserat theory

2021 ◽  
Author(s):  
Jie Ma ◽  
Zhiji Han ◽  
Linsen Yang ◽  
Gaochen Min ◽  
Zhijie Liu ◽  
...  
Keyword(s):  
Dynamics Modeling ◽  
Cosserat Theory

On the Quest for the Best Timoshenko Shear Coefficient

2003 ◽  
Vol 70 (1) ◽  
pp. 154-157 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Correction Factor ◽  
Timoshenko Beam ◽  
Theoretical Basis ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Vibrational Frequencies ◽  
Timoshenko Beam Theory ◽  
Cosserat Theory ◽  
Shear Correction Factor ◽  
Shear Coefficient

Classical Timoshenko beam theory includes a shear correction factor κ which is often used to match natural vibrational frequencies of the beam. In this note, a number of static and dynamic examples are considered which provide a theoretical basis for specifying κ=1. Within the context of Cosserat theory, natural frequencies of the beam can be matched by appropriate specification of the director inertia coefficients with κ=1.

scholarly journals Covariant balance laws in continua with microstructure

2009 ◽  
Vol 63 (1) ◽  
pp. 1-42 ◽  
Author(s):  
Arash Yavari ◽  
Jerrold E. Marsden
Keyword(s):  
Balance Laws ◽  
Continua With Microstructure
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