The new shift perturbation method with applications to vibrational problems

Pakdemirli M.

JVC/Journal of Vibration and Control, vol.30, no.9-10, pp.2225-2236, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 9-10
  • Publication Date: 2024
  • Doi Number: 10.1177/10775463231176400
  • Journal Name: JVC/Journal of Vibration and Control
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2225-2236
  • Keywords: Perturbation methods, the shift perturbation method, nonlinear vibrations, boundary layer problems, Duffing equation
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Employing variable horizontal and vertical shifts for the unperturbed solution, a new perturbation method is proposed. The new method is named as the shift perturbation method. The existing perturbation methods are interpreted with respect to the horizontal and vertical shifts for the unperturbed solution. The new method is applied to some well-known vibrational problems. The method is capable of producing admissible approximate solutions for a wide range of problems such as the free and forced vibrations of the Duffing equation, equations with quadratic and cubic nonlinearities, variable amplitude nonlinear problems, and boundary layer problems. A variant of the method also produced valid solutions for large perturbation parameters.