A Closed form Solution for Nonlinear Oscillators’ Frequencies Using Amplitude-Frequency Formulation

Amin Barari, Amin Kimiaeifar, M.G Nejad, M Motevalli, G Sfahani

Research output: Contribution to journalJournal articleResearchpeer-review

4 Citations (Scopus)

Abstract

Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF) approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM) and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.
Original languageEnglish
JournalShock and Vibration
Volume19
Issue number6
Pages (from-to)1415-1426
Number of pages12
ISSN1070-9622
DOIs
Publication statusPublished - 2012

Keywords

  • Amplitude Frequency Formulation (AFF)
  • Nonlinear Oscillators
  • Analytical Investigations
  • Energy Balanced Method (EBM)

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