Journal ArticleDOI
The response of nonlinear systems to modulated high-frequency input
Samir A. Nayfeh,A. H. Nayfeh +1 more
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TLDR
In this article, the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system was studied.Abstract:
We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.read more
Citations
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The dynamics of systems of complex nonlinear oscillators: a review
Gamal M. Mahmoud,Tassos Bountis +1 more
TL;DR: appropriate perturbation approaches, which have been specially adapted to study periodic solutions, their stability and control, are described and some important applications in physics, mechanics and engineering are mentioned.
Journal ArticleDOI
Bifurcation in an inverted pendulum with tilted high-frequency excitation: analytical and experimental investigations on the symmetry-breaking of the bifurcation
TL;DR: In this paper, the authors investigated the dynamics of an inverted pendulum subjected to high-frequency excitation and analyzed the effect of the tilt of the excitation direction with respect to gravity direction on the bifurcation.
Journal ArticleDOI
Swing-up and stabilization of an underactuated manipulator without state feedback of free joint
TL;DR: A technique without state feedback of the free link is theoretically and experimentally proposed for the swing-up and the stabilization at the upright position of thefree link in a two-link underactuated manipulator.
Journal ArticleDOI
Single-mode control and chaos of cantilever beam under primary and principal parametric excitations
TL;DR: In this paper, a control law based on quantic velocity feedback is proposed to suppress the vibrations of the first mode of a cantilever beam when subjected to primary and principal parametric excitations.
Journal ArticleDOI
On asymptotic properties of systems with strong and very strong high-frequency excitation
TL;DR: In this article, the affect of high-frequency excitation on the low-frequency motions of dynamic systems is considered and several approaches and difficulties connected with the analysis of these systems are shown.
References
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Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Book
Non-linear Vibrations
Günter Schmidt,Aleš Tondl +1 more
TL;DR: In this article, the authors define a set of properties and properties of non-linear systems, including forced, parametric and self-excited vibrations, and investigate their stability in the phase plane.
Journal ArticleDOI
Energy Transfer From High-to Low-Frequency Modes in a Flexible Structure via Modulation
Samir A. Nayfeh,Ali H. Nayfeh +1 more
TL;DR: In this article, an experimental study of axially-symmetric (i.e., circular cross section) cantilever beams to planar external excitations is presented, where one-to-one internal resonances occur at each natural frequency.
Journal ArticleDOI
Coupling between high-frequency modes and a low-frequency mode: Theory and experiment
TL;DR: In this paper, an analytical and experimental investigation into the response of a nonlinear continuous system with widely separated natural frequencies is presented, which is a thin, slightly curved, isotropic, flexible cantilever beam mounted vertically.