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arXiv · 1612.06775

Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment

S. M. Al-Omari·F. D. Zaman·A. Y. Al-Dweik·Ryad A Ghanam
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Abstract

We consider a nonlinear Timoshenko system of partial differential equations (PDEs) with a frictional damping term in rotation angle. The nonlinearity is due to the arbitrary dependence on the rotation moment. A Lie symmetry group classification of the arbitrary function of rotation moment is presented. An optimal system of one-dimensional subalgebras of the nonlinear damped Timoshenko system is derived for all the non-linear cases. All possible invariant variables of the optimal systems for the three non-linear cases are presented. The corresponding reduced systems of ordinary differential equations (ODEs) are also provided.

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S. M. Al-Omari, F. D. Zaman, A. Y. Al-Dweik, Ryad A Ghanam. 2016-12-20. Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment. https://arxiv.org/abs/1612.06775

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