An Itô-based general approximation method for random vibration of hysteretic systems, part I: Gaussian analysis

Noori, Mohammad; Davoodi, H.; Saffar, Ali

doi:10.1016/0022-460x(88)90307-0

Cited by 11 publications

(7 citation statements)

References 20 publications

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“…The specific examples investigated in the paper have been taken from the published literature [18,19], where results for the second-order statistical moments have been given. It has been shown that our computations lead to results that deviate somewhat from the corresponding data given in the sources.…”

Section: Discussionmentioning

confidence: 99%

“…Two particular examples of hysteretic systems taken from the literature [18,19], will constitute the basis for the numerical studies presented here. However, the numerical results that are given in this section, should be considered as preliminary.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The first example is taken from [18]. In this case the equation of motion is given by equations (6) and (7) 3 to a certain extent dominates the termaY\ in equation (9), it was decided, in accordance with the introductory discussion of this section, to investigate the velocity, Y 2 , and hysteretic 'force', Y 3 , separately by replacing equation (9) by the 'decoupled' equation (14) By this, the problem of calculating estimates of the stationary PDFs of Y 2 and Y 3 is reduced to a 2D problem, which is much easier to handle computationally than a full 3D calculation.…”

Section: Examplementioning

confidence: 99%

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The Path Integral Solution Technique Applied to the Random Vibration of Hysteretic Systems

Næss

Johnsen

1991

Computational Stochastic Mechanics

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ABSTRACfIn the paper the path integral solution technique will be described. It is shown how this solution technique can be exploited to provide estimates of the response statistics of nonlinear single-degree-of-freedom dynamic systems excited by white noise or even filtered white noise. The solution technique is singularly well suited to deal with nonlinear systems as there are apparently few limitations on the kind of nonlinearities that can be accomodated. In this paper emphasis is given to the random vibration of hysteretic systems. INTRODUCflONIn recent years there has been a significant progress in the development of numerical methods for providing estimates of the response statistics of nonlinear dynamic systems subjected to random excitation. A fairly good picture of the situation up to 1986 is obtained from the reviews given by Roberts [1.2] and Spencer [3].Markov diffusion processes have played a prominent role in this development work. An important feature of these processes is that their transition probability densities (fPD) and probability density functions (PDF) satisfy a partial differential equation. viz. the Fokker-Planck-Kolmogorov (FPK) equation. Most of the previous research concerned with the application of Markov processes in nonlinear stochastic dynamics has been directed towards a numerical solution of the FPK equation. or the associated Pontryagin-Witt (PW) equations for the statistical moments.An alternative approach to providing the solution of the FPK equation in this context is indicated in a rather inconspicuous note published by Kapitaniak [4]. In that paper the amplitude probability density function of a nonlinear Duffing oscillator P. D. Spanos et al. (eds.), Computational Stochastic Mechanics

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Section: Discussionmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

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The Path Integral Solution Technique Applied to the Random Vibration of Hysteretic Systems

Næss

Johnsen

1991

Computational Stochastic Mechanics

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“…The solution method presented herein is based on an extension of the cumulant-neglect method developed independently by Ibrahim [1], and Wu and Lin [2], which was recently proposed by Noori and Davoodi [3,4] for response analysis of non-linear hysteretic systems.…”

Section: Introductionmentioning

confidence: 99%

“…The procedure for applying the solution method to this system is similar to that used in the previous studies by Noori et al [3,4]. However, unlike the previous studies, in this work the integral expressions for the unknown expected values are solved in a closed form using classical integration procedures.…”

Section: Introductionmentioning

confidence: 99%

Application of an It�-based approximation method to random vibration of a pinching hysteretic system

Noori

Padua²,

Davoodi

1992

Nonlinear Dyn

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In this paper, an extension of the Cumulant-Neglect closure scheme is utilized for the random vibration analysis of a single degree of freedom system with a general pinching hysteresis restoring force. The hysteresis element used in the system model can simulate commonly observed forms of stiffness, strength and pinching degradations. The second order statistics of the system response to a stationary Gaussian white noise input are derived using an It6-based approximation technique. The validity of these response statistics are then verified by comparing them to Monte Carlo simulation results. The numerical studies performed for different combinations of degradation parameters and excitation levels show that the response estimates obtained by this solution method are in good agreement with Monte Carlo simulation. These studies also indicate the applicability of this technique for response analysis of complicated forms of non-linearities.

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A Comprehensive Stationary Non-Gaussian Analysis of BWB Hysteresis

Noori

Davoodi

Baber

1992

Nonlinear Stochastic Mechanics

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An Itô-based general approximation method for random vibration of hysteretic systems, part I: Gaussian analysis

Cited by 11 publications

References 20 publications

The Path Integral Solution Technique Applied to the Random Vibration of Hysteretic Systems

The Path Integral Solution Technique Applied to the Random Vibration of Hysteretic Systems

Application of an It�-based approximation method to random vibration of a pinching hysteretic system

A Comprehensive Stationary Non-Gaussian Analysis of BWB Hysteresis

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