Stochastic averaging: An approximate method of solving random vibration problems

Roberts, J. B.; Spanos, Pol D.

doi:10.1016/0020-7462(86)90025-9

Cited by 483 publications

(170 citation statements)

References 70 publications

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“…The leading order solution U 0 is actually nothing but the result of the stochastic averaging method [34], which roughly assumes that the Hamiltonian is constant along one period of motion. The higher order terms provided by the asymptotic expansion extend the validity of the developments to moderate values of the small parameter, i.e.…”

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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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 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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“…However, the models are not all characterized by hysteretic flow functions. The most ubiquitous of these models, the class of integrate-fire (IF) models, can be heuristically derived from single-neuron dynamics of the form (1), in the limit when the nonlinear term in the dynamics is very weak, so that the potential U(x) is approximately parabolic, using stochastic linearization techniques [5,59]. In the most general case, the "leaky" integrator with threshold, one writes the dynamics in the form [65],…”

Section: I the 'Perfect Integrator' Revisitedmentioning

confidence: 99%

Towards Simplicity: Noise and Cooperation in the Perfect Integrator

Bulsara¹

1994

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“…[8][9][10][11][12] In cases where the stiffness coefficient varies with responses, the analysis becomes complicated because the resulting equations of motion involve nonlinearities. The study of random vibration of nonlinear systems has always been a subject of great interest for researchers, for example, Fokker-Planck-Kolmogorov (FPK) equation method, 13 stochastic averaging methods, 14 equivalent linear method, 15 equivalent nonlinear system method 16 and Monte Carlo method, 17,18 were developed in recent decades.…”

Section: Introductionmentioning

confidence: 99%

Random vibration of vehicle with hysteretic nonlinear suspension under road roughness excitation

Hua

Zhao

et al. 2018

Advances in Mechanical Engineering

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The analysis of random vibration of a vehicle with hysteretic nonlinear suspension under road roughness excitation is a fundamental part of evaluation of a vehicle's dynamic features and design of its active suspension system. The effective analysis method of random vibration of a vehicle with hysteretic suspension springs is presented based on the pseudoexcitation method and the equivalent linearisation technique. A stable and efficient iteration scheme is constructed to obtain the equivalent linearised system of the original nonlinear vehicle system. The power spectral density of the vehicle responses (vertical body acceleration, suspension working space and dynamic tyre load) at different speeds and with different nonlinear levels of hysteretic suspension springs are analysed, respectively, by the proposed method. It is concluded that hysteretic nonlinear suspensions influence the vehicle dynamic characteristic significantly; the frequencyweighted root mean square values at the front and rear suspensions and the vehicle's centre of gravity are reduced greatly with increasing the nonlinear levels of hysteretic suspension springs, resulting in better ride comfort of the vehicle.

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Stochastic averaging: An approximate method of solving random vibration problems

Cited by 483 publications

References 70 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

Towards Simplicity: Noise and Cooperation in the Perfect Integrator

Random vibration of vehicle with hysteretic nonlinear suspension under road roughness excitation

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