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

YILDIZ B., Sınır S., Sınır B. G.

International Journal of Non-Linear Mechanics, cilt.169, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 169
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.ijnonlinmec.2024.104966
  • Dergi Adı: International Journal of Non-Linear Mechanics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Fractional derivative, Fractionally damped model, General solution, Multiple time scale method, Single-degree-of-freedom system
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

This 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.