Journal Article10.1063/5.0051103
Transient probability in basins of noise influenced responses of mono and coupled Duffing oscillators.
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TL;DR: In this paper, the authors proposed a methodology for estimating the probability that a short duration Gaussian white noise can be used to generate or destroy stable modes of a single nonlinear oscillator as well as a set of coupled non-linear oscillators.
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Abstract: Duffing systems excited by harmonic excitations and subjected to noise additions are considered, and it is examined whether the noise addition can be used to steer the response from one stable mode to another. To help with this examination, the authors propose a methodology for estimating the probability that a short duration Gaussian white noise can be used to generate or destroy stable modes of a single nonlinear oscillator as well as a set of coupled nonlinear oscillators. This estimation is done by using the path integral method to find the transient joint probability density function at discrete points in time and then integrating the probability density function over the basins of attraction of the responses of the deterministic system. Results are provided and discussed for the single Duffing oscillator and two coupled Duffing oscillators forced by a near resonance harmonic excitation and noise addition. This work can form a basis for carrying out noise influenced energy movement or localization in the arrays of nonlinear oscillators and have relevance for applications in sensors, energy harvesting devices, and more.
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Citations
Nonlinear Normal Modes of Vibrating Mechanical Systems: 10 Years of Progress
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TL;DR: This review paper summarizes 10 years of progress in nonlinear normal modes of vibrating mechanical systems, covering theoretical and applied aspects, including definitions, construction methods, and applications in aerospace, power, and nanostructures engineering.
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Chaos and subharmonic bifurcations of a soft Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation
Liangqiang Zhou,Fangqi Chen +1 more
TL;DR: In this paper, a soft Duffing oscillator with a non-smooth periodic perturbation and a harmonic excitation is investigated analytically, and it is proved that the system may undergo chaotic motions through infinite or finite odd order subharmonic bifurcations.
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Influence of uncertainties and noise on basins/attractors topology and integrity of Duffing oscillator
Kaio César Borges Benedetti,Paulo B. Gonçalves,Stefano Lenci,Giuseppe Rega +3 more
TL;DR: This study investigates the impact of uncertainties and noise on the Duffing oscillator's global dynamics, employing adaptive phase-space discretization, and examines the effects on basins of attraction, attractors' distributions, and dynamic integrity under harmonic or parametric excitations with added noise and parametric uncertainty.
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Influence of noise on a rotating, softening cantilever beam
Lautaro Cilenti,Maria Cameron,Balakumar Balachandran +2 more
TL;DR: Noise-induced transitions in a rotating, softening cantilever beam exhibit a one-directional behavior.
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Influence of Noise on a Rotating, Softening Cantilever Beam
Lautaro Cilenti,Maria Cameron,Balakumar Balachandran +2 more
- 30 May 2023
TL;DR: In this paper , a large number of trials are used to show that random perturbations can be used to create a transition between a high amplitude response and a low amplitude response of the cantilever, but not vice versa.
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