Similarity reductions of a nonlinear model for vibrations of beams

Camacho, J. C.; Bruzón, María de los Santos

doi:10.3934/proc.2015.0176

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2017

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“…In [14] Humphreys and McKenna considered the existence of multiple periodic solutions for the nonlinear beam Equation (4), while in [15,16] Doole and Hogan transformed the beam Equation (4) into an ordinary differential equation and treated it by using dynamical systems method. Recently, there are also some researches devoted to symmetry group structure and exact solutions of the fourth-order nonlinear beam Equation (4) [17,18].…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry Classification of the Generalized Nonlinear Beam Equation

Huang

2017

Symmetry

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Abstract:In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group theory for the equation under consideration. Lie symmetry reductions of a nonlinear beam-like equation which are singled out from the classification results are investigated. Some classes of exact solutions, including solitary wave solutions, triangular periodic wave solutions and rational solutions of the nonlinear beam-like equations are constructed by means of the reductions and symbolic computation.

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Section: Introductionmentioning

confidence: 99%

Lie Symmetry Classification of the Generalized Nonlinear Beam Equation

Huang

2017

Symmetry

View full text Add to dashboard Cite

show abstract

Similarity reductions of a nonlinear model for vibrations of beams

Cited by 1 publication

References 12 publications

Lie Symmetry Classification of the Generalized Nonlinear Beam Equation

Lie Symmetry Classification of the Generalized Nonlinear Beam Equation

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