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Mathematics 2017, 5(2), 34; doi:10.3390/math5020034

Lie Symmetries, Optimal System and Invariant Reductions to a Nonlinear Timoshenko System

Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
All authors contributed equally to this work.
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Author to whom correspondence should be addressed.
Academic Editor: Johnny Henderson
Received: 2 April 2017 / Revised: 1 June 2017 / Accepted: 12 June 2017 / Published: 17 June 2017
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Abstract

Lie symmetries and their Lie group transformations for a class of Timoshenko systems are presented. The class considered is the class of nonlinear Timoshenko systems of partial differential equations (PDEs). An optimal system of one-dimensional sub-algebras of the corresponding Lie algebra is derived. All possible invariant variables of the optimal system are obtained. The corresponding reduced systems of ordinary differential equations (ODEs) are also provided. All possible non-similar invariant conditions prescribed on invariant surfaces under symmetry transformations are given. As an application, explicit solutions of the system are given where the beam is hinged at one end and free at the other end. View Full-Text
Keywords: Timoshenko beam system; similarity reduction; optimal system; invariant solutions Timoshenko beam system; similarity reduction; optimal system; invariant solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Al-Omari, S.; Zaman, F.; Azad, H. Lie Symmetries, Optimal System and Invariant Reductions to a Nonlinear Timoshenko System. Mathematics 2017, 5, 34.

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