Nonlinear dynamics of self-, parametric, and externally excited oscillator with time delay: van der Pol versus Rayleigh models

Warmiński, Jerzy

doi:10.1007/s11071-019-05076-5

Cited by 42 publications

(14 citation statements)

References 24 publications

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“…Recent theoretical analysis for PA include the effects of quadratic and cubic nonlinearities [7], dualfrequency parametric amplifiers with quadratic and cubic nonlinearities [54], regular and chaotic vibrations with time delay [55], and frequency comb responses [56].…”

Section: Introductionmentioning

confidence: 99%

The effects of nonlinear damping on degenerate parametric amplification

Shaw

2020

Nonlinear Dyn

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This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase between the two. This generalizes and expands on previous studies of nonlinear effects on parametric amplification, notably by including the effects of nonlinear damping, which is commonly observed in a large variety of systems, including micro- and nano-scale resonators. Using the method of averaging, a thorough parameter study is carried out that describes the effects of the amplitudes and relative phase of the two forms of excitation. The effects of nonlinear damping on the parametric gain are first derived. The transitions among various topological forms of the frequency response curves, which can include isolae, dual peaks, and loops, are determined, and bifurcation analyses in parameter spaces of interest are carried out. In general, these results provide a complete picture of the system response and allow one to select drive conditions of interest that avoid bistability while providing maximum amplitude gain, maximum phase sensitivity, or a flat resonant peak, in systems with nonlinear damping.

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Section: Introductionmentioning

confidence: 99%

The effects of nonlinear damping on degenerate parametric amplification

Shaw

2020

Nonlinear Dyn

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“…The vast majority of models for parametric resonance tend to introduce important simplifications of the system in order to fit it into an analytical framework: [ 34 ] uses multiple scale perturbation techniques for a 2-DoF model of a container ship, while [ 38 ] uses Markov and Melnikov approaches; [ 12 ] studies parametric resonance for a 2-DoF model of an archetypal spar buoy, determining nonlinear vibration modes by the application of asymptotic and Galerkin-based methods. Simplified models are successful in predicting the likelihood of parametric resonance, but are less informative about the severity of the parametrically excited response [ 11 , 39 , 42 ], mainly due to the mismatch between the simplified analytical model and the complex real system.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of parametric resonance due to hydrodynamic coupling in a realistic wave energy converter

et al. 2020

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Representative models of the nonlinear behavior of floating platforms are essential for their successful design, especially in the emerging field of wave energy conversion where nonlinear dynamics can have substantially detrimental effects on the converter efficiency. The spar buoy, commonly used for deepwater drilling, oil and natural gas extraction and storage, as well as offshore wind and wave energy generation, is known to be prone to experience parametric resonance. In the vast majority of cases, parametric resonance is studied by means of simplified analytical models, considering only two degrees of freedom (DoFs) of archetypical geometries, while neglecting collateral complexity of ancillary systems. On the contrary, this paper implements a representative 7-DoF nonlinear hydrodynamic model of the full complexity of a realistic spar buoy wave energy converter, which is used to verify the likelihood of parametric instability, quantify the severity of the parametrically excited

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“…Depending on the nature of the loads, the different kinds of excitation can interact. Some attention has been devoted in literature to interactive aeroelastic phenomena, as galloping parametric excitation [31][32][33][34][35][36][37][38][39][40] or galloping vortex-induced vibrations [41][42][43][44][45]. In particular, as regard the former class, the principal resonance of a single-degree-of-freedom system with two-frequency parametric and self-excitation is investigated in [31,34]; the method of multiple scales is used to determine the equations of modulation of amplitude and phase, and qualitative analyses are performed out to study steady state, limit cycle, and torus responses.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear interaction between self- and parametrically excited wind-induced vibrations

Nino

Luongo

2020

Nonlinear Dyn

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The aeroelastic behavior of a planar prismatic visco-elastic structure, subject to a turbulent wind, flowing orthogonally to its plane, is studied in the nonlinear field. The steady component of wind is responsible for a Hopf bifurcation occurring at a threshold critical value; the turbulent component, which is assumed to be a small harmonic perturbation of the former, is responsible for parametric excitation. The interaction between the two bifurcations is studied in a three-dimensional parameter space, made of the two wind amplitudes and the frequency of the turbulence. Aeroelastic forces are computed by the quasi-static theory. A one-D.O.F dynamical system, drawn by a Galerkin projection of the continuous model, is adopted. The multiple scale method is applied, to get a two-dimensional bifurcation equation. A linear stability analysis is carried out to determine the loci of periodic and quasi-periodic bifurcations. Limit cycles and tori are computed by exact, asymptotic, and numerical solutions of the bifurcation equations. Numerical results are obtained for a sample structure, and compared with finite-difference solutions of the original partial differential equation of motion.

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Nonlinear dynamics of self-, parametric, and externally excited oscillator with time delay: van der Pol versus Rayleigh models

Cited by 42 publications

References 24 publications

The effects of nonlinear damping on degenerate parametric amplification

The effects of nonlinear damping on degenerate parametric amplification

Numerical investigation of parametric resonance due to hydrodynamic coupling in a realistic wave energy converter

Nonlinear interaction between self- and parametrically excited wind-induced vibrations

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