Non-linear dynamics of a stochastically excited beam system with impact

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Abstract

The response of non-linear, dynamic systems to stochastic excitation exhibits many interesting characteristics. In thispaper, a strongly non-linear beam-impact system under both broad- and small-banded, Gaussian noise excitations isinvestigated. The response of this system is investigated both numerically, through a multi-degree-of-freedom model, andexperimentally focusing on frequency-domain phenomena such as stochastic equivalents of harmonic and subharmonicsolutions. An improved understanding of these stochastic response characteristics is obtained by comparing these tonon-linear periodic response features of the system. It will be shown that in modelling such a continuous, linear systemwith a local non-linearity, the linear part can be effectively reduced to a description based on several modes. Combining thisreduced, linear part with the local non-linearity in a reduced, non-linear model is shown to result in a non-linear model,which can be used to accurately predict the stochastic response characteristics of the original, continuous, non-linearsystem. It is shown that including more modes to the model causes its response to differ significantly from that of asingle-degree-of-freedom model and show a better correspondence with experimental results, also in the frequency rangeof the first mode.
Original languageEnglish
Pages (from-to)767-779
JournalInternational Journal of Non-Linear Mechanics
Volume38
Issue number5
DOIs
Publication statusPublished - 2003

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Nonlinear Dynamics
Nonlinear Model
Excitation
Degree of freedom
Nonlinearity
Nonlinear Dynamic System
Gaussian Noise
Dynamical systems
Frequency Domain
Correspondence
Harmonic
Model
Predict
Experimental Results
Modeling

Cite this

@article{2509ce06545b496ab9c1e8ed55de34c3,
title = "Non-linear dynamics of a stochastically excited beam system with impact",
abstract = "The response of non-linear, dynamic systems to stochastic excitation exhibits many interesting characteristics. In thispaper, a strongly non-linear beam-impact system under both broad- and small-banded, Gaussian noise excitations isinvestigated. The response of this system is investigated both numerically, through a multi-degree-of-freedom model, andexperimentally focusing on frequency-domain phenomena such as stochastic equivalents of harmonic and subharmonicsolutions. An improved understanding of these stochastic response characteristics is obtained by comparing these tonon-linear periodic response features of the system. It will be shown that in modelling such a continuous, linear systemwith a local non-linearity, the linear part can be effectively reduced to a description based on several modes. Combining thisreduced, linear part with the local non-linearity in a reduced, non-linear model is shown to result in a non-linear model,which can be used to accurately predict the stochastic response characteristics of the original, continuous, non-linearsystem. It is shown that including more modes to the model causes its response to differ significantly from that of asingle-degree-of-freedom model and show a better correspondence with experimental results, also in the frequency rangeof the first mode.",
author = "{Wouw, van de}, N. and {Kraker, de}, A. and {Campen, van}, D.H. and H. Nijmeijer",
year = "2003",
doi = "10.1016/S0020-7462(01)00132-9",
language = "English",
volume = "38",
pages = "767--779",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier",
number = "5",

}

Non-linear dynamics of a stochastically excited beam system with impact. / Wouw, van de, N.; Kraker, de, A.; Campen, van, D.H.; Nijmeijer, H.

In: International Journal of Non-Linear Mechanics, Vol. 38, No. 5, 2003, p. 767-779.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Non-linear dynamics of a stochastically excited beam system with impact

AU - Wouw, van de, N.

AU - Kraker, de, A.

AU - Campen, van, D.H.

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N2 - The response of non-linear, dynamic systems to stochastic excitation exhibits many interesting characteristics. In thispaper, a strongly non-linear beam-impact system under both broad- and small-banded, Gaussian noise excitations isinvestigated. The response of this system is investigated both numerically, through a multi-degree-of-freedom model, andexperimentally focusing on frequency-domain phenomena such as stochastic equivalents of harmonic and subharmonicsolutions. An improved understanding of these stochastic response characteristics is obtained by comparing these tonon-linear periodic response features of the system. It will be shown that in modelling such a continuous, linear systemwith a local non-linearity, the linear part can be effectively reduced to a description based on several modes. Combining thisreduced, linear part with the local non-linearity in a reduced, non-linear model is shown to result in a non-linear model,which can be used to accurately predict the stochastic response characteristics of the original, continuous, non-linearsystem. It is shown that including more modes to the model causes its response to differ significantly from that of asingle-degree-of-freedom model and show a better correspondence with experimental results, also in the frequency rangeof the first mode.

AB - The response of non-linear, dynamic systems to stochastic excitation exhibits many interesting characteristics. In thispaper, a strongly non-linear beam-impact system under both broad- and small-banded, Gaussian noise excitations isinvestigated. The response of this system is investigated both numerically, through a multi-degree-of-freedom model, andexperimentally focusing on frequency-domain phenomena such as stochastic equivalents of harmonic and subharmonicsolutions. An improved understanding of these stochastic response characteristics is obtained by comparing these tonon-linear periodic response features of the system. It will be shown that in modelling such a continuous, linear systemwith a local non-linearity, the linear part can be effectively reduced to a description based on several modes. Combining thisreduced, linear part with the local non-linearity in a reduced, non-linear model is shown to result in a non-linear model,which can be used to accurately predict the stochastic response characteristics of the original, continuous, non-linearsystem. It is shown that including more modes to the model causes its response to differ significantly from that of asingle-degree-of-freedom model and show a better correspondence with experimental results, also in the frequency rangeof the first mode.

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