Analysis of the motion of a rigid rod on a circular surface using interpolated variational iteration method

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COŞKUN S. B., ŞENTÜRK E., ATAY M. T.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.40, no.3, pp.577-584, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.14744/sigma.2022.00062
  • Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.577-584
  • Keywords: Analytical Approximate Solution, Interpolated, Variational Iteration Method, Nonlinear Oscillator, Vibration, Rigid Rod, APPROXIMATE ANALYTICAL SOLUTIONS, AMPLITUDE-FREQUENCY FORMULATION, ADOMIAN DECOMPOSITION METHOD, HOMOTOPY PERTURBATION METHOD, FREE-VIBRATION ANALYSIS, NONLINEAR OSCILLATIONS, ROCKING BACK, SYSTEMS, BEAM
  • Abdullah Gül University Affiliated: Yes

Abstract

In this paper, interpolated variational iteration method (IVIM) is applied to investigate the vibration period and steady-state response for the motion of rigid rod rocking back and forth on a circular surface without slipping. The problem can be considered as a strongly nonlinear oscillator. In this solution procedure, analytical variational iteration technique is utilized by evaluating the integrals numerically. The approximate analytical results produced by the presented method are compared with the other existing solutions available in the literature. The advantage of using numerical evaluation of integrals, the method becomes fast convergent and a highly accurate solution can be obtained within seconds. The authors believe that the presented technique has potentially wide application in the other nonlinear oscillation problems.