Spectral density of oscillator with bilinear stiffness and white noise excitation

Finn Rüdinger, Steen Krenk

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The power spectral density of an oscillator with bilinear stiffness excited by Gaussian white noise is considered. A method originally proposed by Krenk and Roberts [J Appl Mech 66 (1999) 225] relying on slowly changing energy for lightly damped systems is applied. In this method an approximate solution for the power spectral density at a given energy level is obtained by considering local similarity with the free undamped response. The total spectrum is obtained by integrating over all energy levels weighting each with the stationary probability density of the energy. The accuracy of the approximate analytical solution is demonstrated by comparing with results obtained by stochastic simulation. It is shown how the method successfully captures the broadening of the resonance peak and the presence of higher harmonics in the power spectral density of strongly non-linear systems. (C) 2003 Elsevier Ltd. All rights reserved.
Original languageEnglish
JournalProbabilistic Engineering Mechanics
Volume18
Issue number3
Pages (from-to)215-222
ISSN0266-8920
DOIs
Publication statusPublished - 2003

Cite this

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title = "Spectral density of oscillator with bilinear stiffness and white noise excitation",
abstract = "The power spectral density of an oscillator with bilinear stiffness excited by Gaussian white noise is considered. A method originally proposed by Krenk and Roberts [J Appl Mech 66 (1999) 225] relying on slowly changing energy for lightly damped systems is applied. In this method an approximate solution for the power spectral density at a given energy level is obtained by considering local similarity with the free undamped response. The total spectrum is obtained by integrating over all energy levels weighting each with the stationary probability density of the energy. The accuracy of the approximate analytical solution is demonstrated by comparing with results obtained by stochastic simulation. It is shown how the method successfully captures the broadening of the resonance peak and the presence of higher harmonics in the power spectral density of strongly non-linear systems. (C) 2003 Elsevier Ltd. All rights reserved.",
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Spectral density of oscillator with bilinear stiffness and white noise excitation. / Rüdinger, Finn; Krenk, Steen.

In: Probabilistic Engineering Mechanics, Vol. 18, No. 3, 2003, p. 215-222.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Spectral density of oscillator with bilinear stiffness and white noise excitation

AU - Rüdinger, Finn

AU - Krenk, Steen

PY - 2003

Y1 - 2003

N2 - The power spectral density of an oscillator with bilinear stiffness excited by Gaussian white noise is considered. A method originally proposed by Krenk and Roberts [J Appl Mech 66 (1999) 225] relying on slowly changing energy for lightly damped systems is applied. In this method an approximate solution for the power spectral density at a given energy level is obtained by considering local similarity with the free undamped response. The total spectrum is obtained by integrating over all energy levels weighting each with the stationary probability density of the energy. The accuracy of the approximate analytical solution is demonstrated by comparing with results obtained by stochastic simulation. It is shown how the method successfully captures the broadening of the resonance peak and the presence of higher harmonics in the power spectral density of strongly non-linear systems. (C) 2003 Elsevier Ltd. All rights reserved.

AB - The power spectral density of an oscillator with bilinear stiffness excited by Gaussian white noise is considered. A method originally proposed by Krenk and Roberts [J Appl Mech 66 (1999) 225] relying on slowly changing energy for lightly damped systems is applied. In this method an approximate solution for the power spectral density at a given energy level is obtained by considering local similarity with the free undamped response. The total spectrum is obtained by integrating over all energy levels weighting each with the stationary probability density of the energy. The accuracy of the approximate analytical solution is demonstrated by comparing with results obtained by stochastic simulation. It is shown how the method successfully captures the broadening of the resonance peak and the presence of higher harmonics in the power spectral density of strongly non-linear systems. (C) 2003 Elsevier Ltd. All rights reserved.

U2 - 10.1016/S0266-8920(03)00015-8

DO - 10.1016/S0266-8920(03)00015-8

M3 - Journal article

VL - 18

SP - 215

EP - 222

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

IS - 3

ER -