Frequency dependent iteration method for forced nonlinear oscillators

Tien Hoang (1) , Denis Duhamel (1) , Gilles Forêt (1) , Honoré P. Yin (1) , Pierre Argoul (2, 3)

1 navier umr 8205 - Laboratoire Navier
2 IFSTTAR/MAST/SDOA - Sécurité et Durabilité des Ouvrages d'Art
3 LVMT - Laboratoire Ville, Mobilité, Transport

A new iteration method for nonlinear vibrations has been developed by decomposing the periodic solution in two parts corresponding to low and high harmonics. For a nonlinear forced oscillator, the iteration schema is proposed with different formulations for these two parts. Then, the schema is deduced by using the harmonic balance technique. This method has proven to converge to the periodic solutions provided that a convergence condition is satisfied. The convergence is also demonstrated analytically for linear oscillators. Moreover, the new method has been applied to Duffing oscillators as an example. The numerical results show that each iteration schema converges in a domain of the excitation frequency and it can converge to different solutions of the nonlinear oscillator.

Mots clés: Duffing oscillator; iteration procedure; harmonic balance method; Forced nonlinear oscillator

Domaines: Matériaux et structures en mécanique [physics.class-ph]

Tien Hoang, Denis Duhamel, Gilles Forêt, Honoré P. Yin, Pierre Argoul. Frequency dependent iteration method for forced nonlinear oscillators. Applied Mathematical Modelling, 2017, 42, pp.441 - 448. ⟨10.1016/j.apm.2016.10.012⟩. ⟨hal-01695465⟩