𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A modified Mickens iteration procedure for nonlinear oscillators

✍ Scribed by Y.M. Chen; J.K. Liu

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
241 KB
Volume
314
Category
Article
ISSN
0022-460X

No coin nor oath required. For personal study only.

✦ Synopsis

Based on the Mickens procedure, a new iteration scheme is proposed for nonlinear oscillators. Different from the existing Mickens procedures, in the proposed procedure, the algebraic equation governing the frequency of oscillation deduced at each iteration stage is always linear. Taking the Duffing equation as an illustrative example, excellent approximations can be easily obtained. Furthermore, the proposed procedure is extended to obtain the limit cycle of the van der Pol equation. Additionally, a computational disadvantage of the Mickens procedure is eliminated.

πŸ“œ SIMILAR VOLUMES

A classical iteration procedure valid fo
A classical iteration procedure valid for certain strongly nonlinear oscillators
✍ H. Hu; J.H. Tang πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 140 KB

A classical iteration procedure is applied to nonlinear oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. With the procedure, the analytical approximate frequency and the corresponding periodic solution, valid for small as well as large amplitudes of oscillation, c

Solutions of nonlinear oscillators with
Solutions of nonlinear oscillators with fractional powers by an iteration procedure
✍ H. Hu πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 136 KB

A modified iteration procedure is applied to nonlinear oscillations with fractional powers. With the procedure, the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained.