Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

Matteo, Alberto Di; Kougioumtzoglou, Ioannis A.; Pirrotta, Antonina; Spanos, Pol D.; Paola, Mario Di

doi:10.1016/j.probengmech.2014.07.001

Cited by 107 publications

(19 citation statements)

References 34 publications

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“…Spanos and Zeldin [29] put forward a frequency-domain method for the stochastic systems endowed with fractional derivatives. Based on the machinery of the Wiener path integral, Di Matteo et al [30] developed a new approximate analytical technique to determine the nonstationary response probability density function of stochastic oscillators with fractional derivatives term. Agrawal [31] proposed an analytical approach for stochastic dynamic systems with fractional derivative by using the eigenvector expansion method and Laplace transforms.…”

Section: Introductionmentioning

confidence: 99%

Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise

Yang

et al. 2015

Chaos, Solitons & Fractals

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Section: Introductionmentioning

confidence: 99%

Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise

Yang

et al. 2015

Chaos, Solitons & Fractals

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“…Further, the aforementioned technique was extended in [25] to account for multi-degree-of-freedom (MDOF) systems as well as for hysteretic nonlinearities. In [47] the technique was further enhanced and generalized to treat linear and nonlinear systems endowed with fractional derivatives terms.…”

Section: Wiener Path Integral (Wpi) Based Solution Treatmentmentioning

confidence: 99%

Ice Gouge Depth Determination Via an Efficient Stochastic Dynamics Technique

Gazis¹,

Kougioumtzoglou

Patelli

2016

Journal of Offshore Mechanics and Arctic Engineering

Self Cite

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A simplified model of the motion of a grounding iceberg for determining the gouge depth into the seabed is proposed. Specifically, taking into account uncertainties relating to the soil strength, a nonlinear stochastic differential equation governing the evolution of the gouge length/depth in time is derived. Further, a recently developed Wiener path integral (WPI) based approach for solving approximately the nonlinear stochastic differential equation is employed; thus, circumventing computationally demanding Monte Carlo based simulations and rendering the approach potentially useful for preliminary design applications. The accuracy/reliability of the approach is demonstrated via comparisons with pertinent Monte Carlo simulation (MCS) data.

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“…Stochastic perturbations are ubiquitous in the real world, so it is necessary to study the dynamical behaviors of the fractionalorder stochastic systems. A lot of methods have been put forward to study the fractional-order stochastic systems, such as the stochastic averaging method [14][15][16][17], multiple scales method [18][19][20], Wiener path integral technique [21], and statistical linearization-based technique [22]. Some recent articles on this topic are as follows.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Bifurcations of a Fractional‐Order Vibro‐Impact System Driven by Additive and Multiplicative Gaussian White Noises

Yang

Sun

2019

Complexity

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Stochastic fractional-order systems or stochastic vibro-impact systems can present rich dynamical behaviors, and lots of studies dealing with stochastic fractional-order systems or stochastic vibro-impact systems are available now, while the discussion on the stochastic systems with both vibro-impact factors and fractional derivative element is rare. This paper is concerned with the stochastic bifurcation of a fractional-order vibro-impact system driven by additive and multiplicative Gaussian white noises. Firstly, we can remove the discontinuity of the original system with the help of nonsmooth transformation and obtain the equivalent stochastic system. Then, we adopt the stochastic averaging method to get the approximately analytical solutions. At last, an example is discussed in detail to assess the reliability of the developed approach. We also find that the coefficient of restitution factor, fractional derivative coefficient, and fractional derivative order can induce the stochastic bifurcation.

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Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

Cited by 107 publications

References 34 publications

Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise

Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise

Ice Gouge Depth Determination Via an Efficient Stochastic Dynamics Technique

Stochastic Bifurcations of a Fractional‐Order Vibro‐Impact System Driven by Additive and Multiplicative Gaussian White Noises

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