New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators

KARAHAN M. M. F., Pakdemirli M.

International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015, Rhodes, Yunanistan, 23 - 29 Eylül 2015, cilt.1738, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 1738
  • Doi Numarası: 10.1063/1.4952117
  • Basıldığı Şehir: Rhodes
  • Basıldığı Ülke: Yunanistan
  • Anahtar Kelimeler: Cubic-Quintic Duffing Oscillator, Forced Vibrations, Multiple Scales Lindstedt Poincare (MSLP) method, Multiple Scales method, Perturbation Methods, Strongly Nonlinear Systems
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.