Effects of Heave Excitation on Rotations of a Pendulum for Wave Energy Extraction

Horton, Bryan; Wiercigroch, Marian

doi:10.1007/978-1-4020-8630-4_11

Cited by 13 publications

(9 citation statements)

References 12 publications

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“…In fact, interest has been shown for the energy of a system that is governed by a Mathieu equation in the study of a pendulum submitted to wave excitations in [28,47,1] and finds a direct application in the extraction of energy from waves and heave, as also discussed earlier by [17,16]. In the same way, capsizing and rolling motions of ships under stochastic wave excitation can also be assimilated to similar oscillators and are studied by Moshchuk and Troesch in [27,39].…”

Section: The Considered Governing Equationmentioning

confidence: 96%

Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations

Vanvinckenroye

Denoёl

2017

Journal of Sound and Vibration

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a b s t r a c tA linear oscillator simultaneously subjected to stochastic forcing and parametric excitation is considered. The time required for this system to evolve from a low initial energy level until a higher energy state for the first time is a random variable. Its expectation satisfies the Pontryagin equation of the problem, which is solved with the asymptotic expansion method developed by Khasminskii. This allowed deriving closed-form expressions for the expected first passage time. A comprehensive parameter analysis of these solutions is performed. Beside identifying the important dimensionless groups governing the problem, it also highlights three important regimes which are called incubation, multiplicative and additive because of their specific features. Those three regimes are discussed with the parameters of the problem.

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Section: The Considered Governing Equationmentioning

confidence: 96%

Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations

Vanvinckenroye

Denoёl

2017

Journal of Sound and Vibration

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“…For this class of oscillators, the concept of total internal energy plays a central role. It finds applications in wave energy harvesting [5][6][7][8], capsizing and rolling motions of ships under stochastic wave excitation [9,10] and several other biological applications such as protein folding [11]. Using the appropriate non-dimensionalization and discarding the nonlinear governing components, the governing equations of a large number of applications can be cast under the format of Equation (1) where u(t) and w(t) are stochastic processes.…”

Section: X(t) + [1 + U(t)] X(t) = W(t)mentioning

confidence: 99%

Second-order moment of the first passage time of a quasi-Hamiltonian oscillator with stochastic parametric and forcing excitations

Vanvinckenroye

Denoël

2018

Journal of Sound and Vibration

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a b s t r a c tThis work focuses on the stochastic version of the linear Mathieu oscillator with both forced and parametric excitations of small intensity. In this quasi-Hamiltonian oscillator, the concept of energy stored in the oscillator plays a central role and is studied through the first passage time, which is the time required for the system to evolve from a given initial energy to a target energy. This time is a random variable due to the stochastic nature of the loading. The average first passage time has already been studied for this class of oscillator. However, the spread has only been studied under purely parametric excitation. Extending to combinations of both forcing and parametric excitations, this work provides a closed-form solution and a thorough analytical study of the coefficient of variation of the first passage time of the energy in this system. Simple asymptotic solutions are also derived in some particular ranges of parameters corresponding to different regimes.

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“…Indeed, mechanical analogues of physical systems provide a direct visualization of motion allowing an intuitive understanding of the system being studied, as it is done for the analysis of power grid [35] and applications of telecommunications [36]. Rotating motion in the parametric pendulum has also been widely considered in the literature [37], due to the possibility of energy harvesting from sea waves, which would consist in transforming the vertical motion of sea waves in rotating motion of systems composed by parametric pendula [8,38,39,[39][40][41]. The study of stable periodic orbits of Eq.…”

Section: Introductionmentioning

confidence: 99%

Tilted excitation implies odd periodic resonances

et al. 2016

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Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying the Melnikov subharmonic function, we not only determined analytically the loci of saddle-node bifurcations delimiting resonance regions in parameter space, but also explained these observations by demonstrating that, under the Melnikov method point of view, odd resonances arise due to an extra torque that appears in the asymmetric case.

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Effects of Heave Excitation on Rotations of a Pendulum for Wave Energy Extraction

Cited by 13 publications

References 12 publications

Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations

Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations

Second-order moment of the first passage time of a quasi-Hamiltonian oscillator with stochastic parametric and forcing excitations

Tilted excitation implies odd periodic resonances

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