Asymptotic expansion of ship capsizing in random sea waves—I. First-order approximation

Moshchuk, Nikolai; Ibrahim, R. A.; Khas’minskiĭ, R. Z.; Chow, Pao–Liu

doi:10.1016/0020-7462(95)00021-f

Cited by 22 publications

(13 citation statements)

References 13 publications

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“…However, the mean first passage time of a stochastic system through the boundary ∂ of a given domain , to which the system belongs at initial state, is ruled by the Pontryagin equation, see Section 2. Many solutions of more or less complex problems in terms of mean first passage time can be found in the literature [6,35,25,26,22]. Among them the first passage time for a stochastic fractional derivative system with power-law restoring force [22] shows the typical range of difficulties that can be tackled today.…”

Section: First Passage Time Of the Parametric And Forced Oscillatorsmentioning

confidence: 99%

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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: First Passage Time Of the Parametric And Forced Oscillatorsmentioning

confidence: 99%

“…Following the matched asymptotic expansion solution applied in [25,26] to the capsizing of boats in random seas (with external forcing only, though), a composite solution to (13) is provided as the sum of the outer and inner solutions…”

Section: The Higher Order Derivative In {·} mentioning

confidence: 99%

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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“…The asymptotic expansion method developed by Moshchuk in (Moshchuk, et al, 1995a) and (Moshchuk, et al, 1995b) solves equation (7) for an approximate form of the first passage time:…”

Section: Average First Passage Timementioning

confidence: 99%

“…As the excitation is stochastic, the first passage time is a random variable. An asymptotic expansion method was developed by Moshchuk in (Moshchuk, et al, 1995a) and (Moshchuk, et al, 1995b) to approximate the mean first passage time of a nonlinear stochastic process representing a ship motion on random sea waves. Chunbiao and Liu developed in respectively (Chunbiao & Bohou, 2000) and (Liu, et al, 2013) the stochastic averaging method for quasi-nonintegrable-hamiltonian systems submitted to Gaussian and Poisson white noises and Li extended this approach to stochastic fractional derivative systems with power-form restoring force in (Li, et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…The quasi-Hamiltonian system is characterized by a set of Itô differential equations (Schuss, 2010) and the first passage time is obtained by solution of the corresponding Pontryagin equation (Moshchuk, et al, 1995a) and (Moshchuk, et al, 1995b). Finally, the accuracy of the expansion is illustrated by comparison with Monte Carlo simulations of the motion.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic rotational stability of tower cranes under gusty winds

Vanvinckenroye

Denoël

2016

Insights and Innovations in Structural Engineering, Mechanics and Computation

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Pendulum energy converter excited by random loads

et al. 2017

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We present new solutions for the dynamics of a pendulum energy converter which is vertically excited at its suspension point. Thereby, we deal with a random excitation by a non‐white Gaussian stochastic process. We formulate the pendulum energy converter as a weakly perturbed Hamiltonian system. The random process across the energy levels of the Hamiltonian system is then approximated by a Markov process, which is obtained by stochastic averaging. This procedure leads to analytical results for the energy of the pendulum motion, which are used for analyzing the required probability of reaching higher energy states of the pendulum energy converter in order to maximize the harvested energy.

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Asymptotic expansion of ship capsizing in random sea waves—I. First-order approximation

Cited by 22 publications

References 13 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

Stochastic rotational stability of tower cranes under gusty winds

Pendulum energy converter excited by random loads

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