Journal ArticleDOI
The Response of a Single-Degree-of-Freedom System with Quadratic and Cubic Non-Linearities to a Fundamental Parametric Resonance
TLDR
In this paper, the response of a one-degree-of-freedom system with quadratic and cubic nonlinearities to a principal parametric resonance is investigated, and the results are verified by integrating the governing equation with use of a digital computer and an analogue computer.About:
This article is published in Journal of Sound and Vibration.The article was published on 1988-01-08. It has received 94 citations till now. The article focuses on the topics: Attractor & Bifurcation diagram.read more
Citations
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Journal ArticleDOI
The Non-Linear Response of a Slender Beam Carrying a Lumped Mass to a Principal Parametric Excitation: Theory and Experiment
TL;DR: In this article, the Euler-Bernoulli theory for a slender beam is used to derive the governing non-linear partial differential equation for an arbitrary position of the lumped mass.
Journal ArticleDOI
Nonlinear response of a parametrically excited buckled beam
TL;DR: In this paper, a nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented, and the results are verified by integrating the governing equation using both digital and analog computers.
Journal ArticleDOI
Quasi-Periodic Oscillations, Chaos and Suppression of Chaos in a Nonlinear Oscillator Driven by Parametric and External Excitations
Mohamed Belhaq,M. Houssni +1 more
TL;DR: In this paper, the generalized averaging method is applied to reduce the original quasi-periodically driven system to a periodically driven one, and then multiple-scale perturbation is applied in a second step to approximate the periodic solutions of the reduced periodically driven system.
Journal ArticleDOI
Bifurcations and chaos in parametrically excited single-degree-of-freedom systems
TL;DR: In this paper, the behavior of single-degree-of-freedom systems possessing quadratic and cubic nonlinearities subject to parametric excitation is investigated, and a global bifurcation diagram in the excitation amplitude and excitation frequency domain is presented showing different possible stable steady state solutions (attractors).
Journal ArticleDOI
Single-Mode Control of a Cantilever Beam Under Principal Parametric Excitation
Shafic S. Oueini,H.A. Nayfeh +1 more
TL;DR: In this article, a control law based on cubic velocity feedback is proposed to suppress the vibrations of the first mode of a cantilever beam when subjected to a principal parametric resonance.
References
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Book
Perturbation Methods
Ali H. Nayfeh,Vimal Singh +1 more
TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
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.
Journal ArticleDOI
Parametric Random Vibration
TL;DR: This monograph is a state of the art presentation of parametric random vibration, based on an enormous number of published papers and reports, and provides the necessary tools for deriving response statistical functions and techniques for examining stochastic parameter stability, as required in later chapters.
Journal ArticleDOI
Suppression of period doubling in symmetric systems
James W. Swift,Kurt Wiesenfeld +1 more
TL;DR: The role of symmetry in systems displaying period-doubling instabilities was examined in this article, where it was found that symmetric orbits will not undergo period doubling except in extraordinary cases.
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.