Parametric roll vulnerability of ships using Markov and Melnikov approaches

Somayajula, Abhilash; Falzarano, Jeffrey

doi:10.1007/s11071-019-05090-7

Cited by 10 publications

(4 citation statements)

References 42 publications

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“…In the case of a floating body, changes are due to variations of the wetted surface, determined by the relative movement of the floater with respect to the wave field. 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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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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“…Substituting equations (7), ( 8) and (19) into equation (4), one has the approximate equivalent integer-order system by remaining the first-order harmonic terms, as shown below It is worth noting that the research results indicate that Criterion 1 is a necessary rather than sufficient condition for the generation of genuine chaos [29][30][31][32][33][34][35]. That is, if the system (22) has chaotic behavior, its Melnikov function ( ) M t 0 must have a simple zero point.…”

Section: Approximate Equivalent Integer-order Systemmentioning

confidence: 99%

“…Although Melnikov approach only provides an approximate result, it is still one of few techniques allowing analytical prediction of chaos occurrence. For IO deterministic and stochastic systems, there have been many research results on the application of Melnikov theory [30][31][32][33]. However, for FO dynamical systems, the application of Melnikov theory is still relatively rare.…”

Section: Introductionmentioning

confidence: 99%

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

Huang

2023

Phys. Scr.

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The dynamical behavior of Liénard systems has always been a hot topic in nonlinear analysis. In the present study, a simple fractional-order feedback controller is put forward to tame chaos for a class of forced generalized Liénard systems. Adopting harmonic balance method, the first-order approximate equivalent integer-order system of the original fractional-order system is deduced. Then the criterion for taming chaos is established by employing the Melnikov approach. Duffing-Rayleigh chaotic oscillator is taken as an example to illustrate the validity of the proposed method. Firstly, the critical feedback intensity and differential order for taming chaos are obtained by the proposed criterion. Then, multiple numerical indicators such as phase portrait, time history plot, Lyapunov exponent and bifurcation diagram are provided to assist in analyzing theoretical results.

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“…Compared with wind, waves are accompanied by more randomness, as they are a vibration physically (instead of flow) [14]. Ocean engineering has adopted various wave spectrum (e.g., Bretschneider spectrum) to approximate complex waves [15]. Each random wave combines of dozens of regular waves (with a single frequency and the corresponding amplitude), while each of the waves are of the corresponding random phase.…”

Section: Introductionmentioning

confidence: 99%

A Stackable Triboelectric Nanogenerator for Wave-Driven Marine Buoys

et al. 2022

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Marine distributed devices are essential infrastructure for exploring and utilizing the ocean. As the most common carrier of these devices, floating and submerged buoys are subject to a bottleneck of power supply. Recent progress in nanogenerators could convert the high-entropy marine kinetic energy (e.g., wave) robustly, which may form an in-situ power solution to marine distributed devices. This study is devoted to develop a stackable triboelectric nanogenerator (S-TENG), while each layer of it is made into multiple channels carrying PTFE balls in between Aluminum electrodes. In the experiments based on forced motion, the peak power density of the S-TENG reaches 49 W/m3, about 29% promotion from our previous benchmark. The S-TENG has also become less vulnerable to directional variation of the excitation, making its integration on various platforms more flexible in real conditions. In practice, the S-TENG has demonstrated its capability of powering LEDs as well as various sensors measuring salinity, temperature and acidity, which means the S-TENG could self-power many compact marine buoys.

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Parametric roll vulnerability of ships using Markov and Melnikov approaches

Cited by 10 publications

References 42 publications

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

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

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

A Stackable Triboelectric Nanogenerator for Wave-Driven Marine Buoys

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