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A general solution procedure for nonlinear single degree of freedom systems including fractional derivatives

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  • NSTL
  • Elsevier
© 2024 Elsevier LtdThis paper considers oscillations of systems with a single-degree-of-freedom (SDOF) including fractional derivatives. The system is assumed to be an unforced condition. A general solution procedure that can be effectively applied to various types of fractionally damped models, where damping is defined by a fractional derivative, in engineering and physics is proposed. The nonlinearity of the mentioned models contains not only damping but can also consist of acceleration or displacement. This study proposed a new general model that includes but not limited to modified fractional versions of the well-known linear, quadratic, Coulomb and negative damped models. The method of multiple time scales is performed to obtain approximate analytical solutions. The solution, the amplitude, and the phase in the applications are plotted for various fractional derivative parameter values. In order to confirm their validity, our results for the case of the fractional derivative parameter equal to one are compared with others available in the literature.

Fractional derivativeFractionally damped modelGeneral solutionMultiple time scale methodSingle-degree-of-freedom system

Yildiz B.、Sinir S.、Sinir B.G.

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Department of Mathematics Faculty of Science Bilecik Şeyh Edebali University

General Coordination Office of Project İzmir Katip Çelebi University

Department of Civil Engineering Faculty of Engineering Manisa Celal Bayar University

2025

10.1016/j.ijnonlinmec.2024.104966

International journal of non-linear mechanics

International journal of non-linear mechanics

SCI
ISSN：0020-7462
年,卷(期)：2025.169(Feb.)
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