Forced vibrations of strongly nonlinear systems with multiple scales lindstedt poincare method

Pakdemirli M., KARAHAN M. M. F., Boyaci H.

Mathematical and Computational Applications, cilt.16, sa.4, ss.879-889, 2011 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 4
  • Basım Tarihi: 2011
  • Doi Numarası: 10.3390/mca16040879
  • Dergi Adı: Mathematical and Computational Applications
  • Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.879-889
  • Anahtar Kelimeler: Forced vibrations, Lindstedt poincare method, Multiple scales method, Numerical solutions, Perturbation methods, Strongly nonlinear systems
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate solutions. For the case of weak and strong nonlinearities, approximate solutions of the new method are contrasted with the usual Multiple Scales (MS) method and numerical simulations. For weakly nonlinear systems, frequency response curves of both perturbation methods and numerical solutions are in good agreement. For strongly nonlinear systems however, results of MS deviate much from the MSLP method and numerical simulations, the latter two being in good agreement. Keywords- Perturbation Methods, Lindstedt Poincare method, Multiple. © Association for Scientific Research.