Effects of External Excitation Frequency Variations on the Vibrations of a Cubic Nonlinear Equation

Pakdemirli M.

Romanian Journal of Acoustics and Vibration, vol.22, no.1, pp.32-38, 2025 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 1
  • Publication Date: 2025
  • Journal Name: Romanian Journal of Acoustics and Vibration
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Aerospace Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.32-38
  • Keywords: forced vibrations, frequency variation, nonlinear dynamics, perturbation methods
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

The effect of external excitation frequency variation on the vibrations of a damped cubic nonlinear equation is investigated. Three types of frequency variations are considered: Decaying type variation, built-in type variation, and harmonic variation. Approximate solutions are constructed using the Method of Multiple Scales. Steady-state deterministic solutions are possible in the first two cases for long time scales. In the harmonic variation case, steady-state solutions are not possible, and the amplitudes and phases do not tend to a constant value. Direct integration of the model depicts the chaotic behavior of the system.