On dynamics of elastic rod based on exact Cosserat model |
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| Authors: | Liu Yan-Zhu |
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| Affiliation: | Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China |
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| Abstract: | The analysis of kinematics and dynamics of an elastic rod with
circular cross section is studied on the basis of exact Cosserat
model under consideration of the tension and shear deformation of
the rod. The dynamical equations of a rod with arbitrary initial
shape are established in general form. The dynamics of a straight
rod under axial tension and torsion is discussed as an example. In
discussion of static stability in the space domain the Greenhill
criteria of stability and the Euler load are corrected by the
influence of tension and shear strain. In analysis of dynamical
stability in the time domain it is shown that the Lyapunov and Euler
stability conditions of the rod in space domain are the necessary
conditions of Lyapunov's stability in the time domain. The longitudinal,
torsional and lateral vibrations of a straight rod based on exact
model are discussed, and an exact formula of free frequency of
lateral vibration is obtained. The free frequency formulas of
various simplified models, such as the Rayleigh beam, the Kirchhoff
rod, and the Timoshenko beam, can be seen as special cases of the
exact formula under different conditions of simplification. |
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| Keywords: | dynamics of elastic rod exact Cosserat model lateral vibration of rod |
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