Invariant properties of Timoshenko beam equations

The Lie groups theory is applied to study the invariant properties of the Timoshenko beam equations. A group classification with respect to the external load is performed and the full symmetry groups are determined. Then, the most general form of the solutions to the Timoshenko beam equations, invar...

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Bibliographic Details
Published in:International journal of engineering science 1995-11, Vol.33 (14), p.2103-2114
Main Author: Djondjorov, Peter A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
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Summary:The Lie groups theory is applied to study the invariant properties of the Timoshenko beam equations. A group classification with respect to the external load is performed and the full symmetry groups are determined. Then, the most general form of the solutions to the Timoshenko beam equations, invariant under an arbitrary one-parameter symmetry group is obtained. As an example, invariant solutions, representing travelling waves along the beam are discussed. Next, for each case of external loads, specified during the group classification procedure, the variational and divergence symmetries of the governing equations are determined. Finally, eight conservation laws for the solutions to the Timoshenko beam equations are derived via the Noether theorem, each being valid for a particular choice of the external load.
ISSN:0020-7225
1879-2197
DOI:10.1016/0020-7225(95)00056-4