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

Shadi Al-Omari, Fiazuddin Zaman and Hassan Azad
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Shadi Al-Omari: Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Fiazuddin Zaman: Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Hassan Azad: Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Mathematics, 2017, vol. 5, issue 2, 1-12

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.

Keywords: Timoshenko beam system; similarity reduction; optimal system; invariant solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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