Effect of Slow Parameter Variations on the Vibrations of a Duffing Equation

Pakdemirli M.

Romanian Journal of Acoustics and Vibration, cilt.21, sa.1, ss.27-34, 2024 (ESCI, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 1
  • Basım Tarihi: 2024
  • Dergi Adı: Romanian Journal of Acoustics and Vibration
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Aerospace Database, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.27-34
  • Anahtar Kelimeler: - Nonlinear Vibrations, Free and Forced Vibrations, Method of Multiple Scales, Transient Solutions, Slow Parameter Variation
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Free and forced damped vibrations of a Duffing equation with cubic nonlinearities is considered. The damping, nonlinearity and external excitation parameters are assumed to vary slowly in time. Using the Method of Multiple Scales, a perturbation technique, the amplitude and phase modulation equations are derived in its most general case. First, the free vibration case is treated. Decaying, built-up and harmonically varying functions are taken to model the slow variations of the parameters in time. The amplitude and phase modulation equations can be integrated to obtain closed form solutions in general for free vibrations. For the forced vibrations, a resort to the numerical techniques is required for the integration of the amplitude and phase modulation equations. It is shown that slow variations on the coefficients may lead to substantial changes in the dynamics of the problem.