NDLI: Autoresonant dynamics of weakly coupled oscillators

Content Provider	Springer Nature Link
Author	Manevitch, Leonid I. Kovaleva, Agnessa
Copyright Year	2015
Abstract	This paper studies the emergence of autoresonance (AR) in a two-degrees-of-freedom system consisting of an excited nonlinear actuator (the Duffing oscillator) linearly coupled to a passive linear oscillator. Two classes of system are considered: (1) In the system of the first type, a periodic force with constant (resonance) frequency is applied to the nonlinear (Duffing) oscillator with slowly time-decreasing linear stiffness; (2) in the system of the second type, the nonlinear oscillator with constant parameters is excited by a force with slowly increasing frequency. In both cases, the linear oscillator and the linear coupling are time-invariant, and the system is initially engaged in resonance. In the first step, the dynamics of the undamped system is analyzed. It is shown here that in the system of the first type, AR may occur in both oscillators, but in the system of the second type, the amount of energy transferred from the nonlinear oscillator is insufficient to excite high-energy motion in the attached oscillator. Different dynamical behavior arises due to different resonance properties of the systems. In the next step, an effect of viscous damping in the oscillators and the coupling is investigated. As this paper demonstrates, the response enhancement may be observed in the system of the first type on a bounded time interval provided that dissipation is weak enough. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is proved.
Starting Page	683
Ending Page	695
Page Count	13
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	84
Issue Number	2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-11-30
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear oscillations Asymptotic methods Autoresonance Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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