Stochastic analysis of self-induced vibrations

Finn Rüdinger, Steen Krenk

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Vortex-induced vibrations of a structurl element are modelled as a non-linear stochastic single-degree-of-freedom system. The deterministic part of the governing equation represents laminar flow conditions with a stationary non-zero solution corresponding to lock-in. Across-wind turbulence is included asd an additive excitation and along-wind turbulence is introduced as a parametric excitation term, both assumed to be white noise processes. An approximate solution to the corresponding Fokker-Planck equation in terms of the stationary probability density of the energy is obtained. The auto spectral density of the position at a particualr energy level is approximated by the spectral density of a linear system with energy dependent damping. The spectral density is then obtained by integration of the energy conditional spectral density over all energies weighted by the probability density. The approximate theoretical expressions for the probability density of the energy and the auto spectral density of the position compare favourably with results obtained by numerical simulation.
Original languageEnglish
JournalMeccanica
VolumeVol. 37
Pages (from-to)pp. 3-14
ISSN0025-6455
Publication statusPublished - 2002

Cite this

Rüdinger, Finn ; Krenk, Steen. / Stochastic analysis of self-induced vibrations. In: Meccanica. 2002 ; Vol. Vol. 37. pp. pp. 3-14.
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abstract = "Vortex-induced vibrations of a structurl element are modelled as a non-linear stochastic single-degree-of-freedom system. The deterministic part of the governing equation represents laminar flow conditions with a stationary non-zero solution corresponding to lock-in. Across-wind turbulence is included asd an additive excitation and along-wind turbulence is introduced as a parametric excitation term, both assumed to be white noise processes. An approximate solution to the corresponding Fokker-Planck equation in terms of the stationary probability density of the energy is obtained. The auto spectral density of the position at a particualr energy level is approximated by the spectral density of a linear system with energy dependent damping. The spectral density is then obtained by integration of the energy conditional spectral density over all energies weighted by the probability density. The approximate theoretical expressions for the probability density of the energy and the auto spectral density of the position compare favourably with results obtained by numerical simulation.",
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Rüdinger, F & Krenk, S 2002, 'Stochastic analysis of self-induced vibrations', Meccanica, vol. Vol. 37, pp. pp. 3-14.

Stochastic analysis of self-induced vibrations. / Rüdinger, Finn; Krenk, Steen.

In: Meccanica, Vol. Vol. 37, 2002, p. pp. 3-14.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Stochastic analysis of self-induced vibrations

AU - Rüdinger, Finn

AU - Krenk, Steen

PY - 2002

Y1 - 2002

N2 - Vortex-induced vibrations of a structurl element are modelled as a non-linear stochastic single-degree-of-freedom system. The deterministic part of the governing equation represents laminar flow conditions with a stationary non-zero solution corresponding to lock-in. Across-wind turbulence is included asd an additive excitation and along-wind turbulence is introduced as a parametric excitation term, both assumed to be white noise processes. An approximate solution to the corresponding Fokker-Planck equation in terms of the stationary probability density of the energy is obtained. The auto spectral density of the position at a particualr energy level is approximated by the spectral density of a linear system with energy dependent damping. The spectral density is then obtained by integration of the energy conditional spectral density over all energies weighted by the probability density. The approximate theoretical expressions for the probability density of the energy and the auto spectral density of the position compare favourably with results obtained by numerical simulation.

AB - Vortex-induced vibrations of a structurl element are modelled as a non-linear stochastic single-degree-of-freedom system. The deterministic part of the governing equation represents laminar flow conditions with a stationary non-zero solution corresponding to lock-in. Across-wind turbulence is included asd an additive excitation and along-wind turbulence is introduced as a parametric excitation term, both assumed to be white noise processes. An approximate solution to the corresponding Fokker-Planck equation in terms of the stationary probability density of the energy is obtained. The auto spectral density of the position at a particualr energy level is approximated by the spectral density of a linear system with energy dependent damping. The spectral density is then obtained by integration of the energy conditional spectral density over all energies weighted by the probability density. The approximate theoretical expressions for the probability density of the energy and the auto spectral density of the position compare favourably with results obtained by numerical simulation.

M3 - Journal article

VL - Vol. 37

SP - 3

EP - 14

JO - Meccanica

JF - Meccanica

SN - 0025-6455

ER -