Stochastic synchronization of rotating parametric pendulums

Alevras, Panagiotis; Yurchenko, Daniil; Næss, Arvid

doi:10.1007/s11012-014-9955-4

Cited by 10 publications

(7 citation statements)

References 39 publications

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“…When the parameter e equals zero, the dimensionless Eqs. (14) and (16) turns into the equation found in [1][2][3][4]. It also means that when the maximum angle of u approaches zero, the excitation by the crank-shaftslider becomes a harmonic excitation similarly to the classical parametrically excited pendulum.…”

Section: Vibrating System Description and Governing Equations Of Motionsmentioning

confidence: 94%

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Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

et al. 2015

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The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crankshaft -slider mechanism. The novelty is the obtainment and analysis of a mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crankshaft -slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crankshaft -slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations-rotations and chaotic motions.

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Section: Vibrating System Description and Governing Equations Of Motionsmentioning

confidence: 94%

“…In Alevras et al [16] it was analyzed the dynamics of two pendulums on a block linked to a base with a damper and a spring. The base is excited by a sinusoidal force, thus provoking a stochastic parametric excitation of the pendulums.…”

Section: Introductionmentioning

confidence: 99%

Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

et al. 2015

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“…Because of the way how phenomenon was discovered, synchronization is closely connected with pendulums. In the papers [1,10,16] results for synchronization phenomenon in case of rotating parametric pendulums are presented, whereas, the problem of rotational motion in different and the same direction of the pendulums is described in [5]. Furthermore, co-and counter-rotating coupled spherical pendulums is studied in [28].…”

Section: Introductionmentioning

confidence: 99%

Vibration, synchronization and localization of three-bladed rotor: theoretical and experimental studies

Szmit

2021

Eur. Phys. J. Spec. Top.

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Numerical and experimental methods in free and forced vibrations of the rotating structure consisting of the rigid hub and three flexible beams are considered. Firstly, the system of four mutually coupled dimensionless differential governing equations is presented and then forced response of the system as well as synchronization phenomenon are investigated. Next, the finite elements method is used to design the rotating structure and analyse complex dynamic response. During the numerical calculations symmetric, as well as de-tuned rotor are analyzed. Finally, results obtained from ordinary differential equations and numerical simulations are compared with experimental tests.

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“…Recently the authors have published a number of papers where a stochastic excitation has been used to model the parametrically excited pendulum behavior under more realistic loading [22][23][24][25][26]. Namely, a harmonic excitation with a mean frequency and random phase modulations has been used to generate a sea like waves with a proper spectrum (Pierson-Moskowitz spectrum was used).…”

Section: Introductionmentioning

confidence: 99%

Parametric pendulum based wave energy converter

Yurchenko

Alevras

2018

Mechanical Systems and Signal Processing

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The paper investigates the dynamics of a novel wave energy converter based on the parametrically excited pendulum. The herein developed concept of the parametric pendulum allows reducing the influence of the gravity force thereby significantly improving the device performance at a regular sea state, which could not be achieved in the earlier proposed original point-absorber design. The suggested design of a wave energy converter achieves a dominant rotational motion without any additional mechanisms, like a gearbox, or any active control involvement. Presented numerical results of deterministic and stochastic modeling clearly reflect the advantage of the proposed design. A set of experimental results confirms the numerical findings and validates the new design of a parametric pendulum based wave energy converter. Power harvesting potential of the novel device is also presented.

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Stochastic synchronization of rotating parametric pendulums

Cited by 10 publications

References 39 publications

Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

Vibration, synchronization and localization of three-bladed rotor: theoretical and experimental studies

Parametric pendulum based wave energy converter

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