Journal ArticleDOI
Response of self-excited oscillators to multifrequency excitations
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TLDR
In this article, the authors used the method of multiple scales to determine the response of a self-excited system having a single degree of freedom to multi-frequency harmonic excitations.About:
This article is published in Journal of Sound and Vibration.The article was published on 1981-12-22. It has received 10 citations till now. The article focuses on the topics: Multiple-scale analysis & Amplitude.read more
Citations
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The response of non-linear single-degree-of-freedom systems to multifrequency excitations
TL;DR: In this article, the response of single-degree-of-freedom systems with cubic nonlinearities to excitations that involve multiple frequencies is analyzed and conditions for the existence and stability of steady-state solutions are determined.
Journal ArticleDOI
Simultaneous resonances in non-linear structural vibrations under two-frequency excitation
TL;DR: In this paper, a system of equations with quadratic and cubic nonlinearities is considered, which models structural elements having initial curvature and exhibiting mid-surface stretching during motion.
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Response of self-excited two-degree-of-freedom systems to multifrequency excitations
TL;DR: In this paper, the response to multifrequency excitation of a two-degree-of-freedom self-excited system is analyzed by using the method of multiple scales, and three cases of resonance are considered: superharmonic, primary, and subharmonic.
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Parametrically excited non-linear systems: a comparison of two methods
TL;DR: Subharmonic resonance of two-degree-of-freedom systems with cubic non-linearities to multifrequency parametric excitations in the presence of three-to-one internal resonance is investigated.
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Parametrically excited nonlinear systems: a comparison of two methods
TL;DR: In this paper, two approximate methods (the multiple scales and the generalized synchronization) are used to construct a first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases.
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.