Autoresonance energy transfer versus localization in weakly coupled oscillators

Autor:	Kovaleva, Agnessa, Manevitch, Leonid
Rok vydání:	2014
Předmět:	Nonlinear Sciences - Pattern Formation and Solitons Nonlinear Sciences - Chaotic Dynamics 05.45.Xt
Druh dokumentu:	Working Paper
Popis:	In this paper we investigate the distribution of energy between weakly coupled linear and nonlinear oscillators in a two-degree-of-freedom (2D) system. Two classes of problems are studied analytically and numerically: (1) a periodic force with constant frequency is applied to the nonlinear (Duffing) oscillator with slowly time-decreasing linear stiffness; (2) the time-independent nonlinear oscillator is excited by a force with slowly increasing frequency. In both cases, stiffness of the attached linear oscillator and linear coupling remain constant, and the system is initially engaged in resonance. This paper demonstrates that in the systems of the first type autoresonance (AR) occurs in both oscillators while in systems of the second type AR occurs only in the excited nonlinear oscillator but the coupled linear oscillator exhibits small bounded oscillations. Considering slow detuning, we obtain explicit asymptotic approximations for the amplitudes and the phases of oscillations close to exact (numerical) results. Comment: 6 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1410.6098 Zobrazit plný text záznamu View this record from Arxiv