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Al-Omari, Shadi; Zaman, Fiazuddin; Azad, Hassan

Lie symmetries, optimal system and invariant reductions to a nonlinear Timoshenko system. (English) Zbl 1367.35014

Mathematics 5, No. 2, Paper No. 34, 12 p. (2017).
Summary: 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.

Cited in 1 Document

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

Keywords:

Timoshenko beam system; similarity reduction; optimal system; invariant solutions; one-dimensional sub-algebras; explicit solutions

Software:

Janet
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References:

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