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The ‘damping effect’ in the dynamic response of stochastic oscillators

Sondipon Adhikari, Blanca Pascual

Probabilistic Engineering Mechanics, Volume: 44, Pages: 2 - 17

Swansea University Author: Sondipon Adhikari

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DOI (Published version): 10.1016/j.probengmech.2015.09.017

Abstract

We consider the dynamics of linear damped oscillators with stochastically perturbed natural frequencies. When average dynamic response is considered, it is observed that stochastic perturbation in the natural frequency manifests as an increase of the effective damping of the system. Assuming uniform...

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Published in: Probabilistic Engineering Mechanics
ISSN: 0266-8920
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa28973
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first_indexed 2016-06-21T18:24:34Z
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spelling 2018-01-19T18:19:55.9719021 v2 28973 2016-06-21 The ‘damping effect’ in the dynamic response of stochastic oscillators 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2016-06-21 FGSEN We consider the dynamics of linear damped oscillators with stochastically perturbed natural frequencies. When average dynamic response is considered, it is observed that stochastic perturbation in the natural frequency manifests as an increase of the effective damping of the system. Assuming uniform distribution of the natural frequency, a closed-from expression of equivalent damping for the mean response has been derived to explain the ‘increasing damping’ behaviour. In addition to this qualitative analysis, a comprehensive quantitative analysis is proposed to calculate the statistics of frequency response functions from the probability density functions of the natural frequencies. Firstly, single-degree-of-freedom-systems are considered and closed-form analytical expressions for the mean and variance are obtained using a hybrid Laplace's method. Several probability density functions, including gamma, normal and lognormal distributions, are considered for the derivation of the analytical expressions. The method is extended to calculate the mean and the variance of the frequency response function of multiple-degrees-of-freedom dynamic systems. Proportional damping is assumed and the eigenvalues are considered to be independent. Results are derived for several probability density functions and damping factors. The accuracy of the approach for both single and multiple-degrees-of-freedom systems is examined using the direct Monte Carlo simulation. Journal Article Probabilistic Engineering Mechanics 44 2 17 0266-8920 30 4 2016 2016-04-30 10.1016/j.probengmech.2015.09.017 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2018-01-19T18:19:55.9719021 2016-06-21T12:41:31.9339630 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Sondipon Adhikari 1 Blanca Pascual 2
title The ‘damping effect’ in the dynamic response of stochastic oscillators
spellingShingle The ‘damping effect’ in the dynamic response of stochastic oscillators
Sondipon Adhikari
title_short The ‘damping effect’ in the dynamic response of stochastic oscillators
title_full The ‘damping effect’ in the dynamic response of stochastic oscillators
title_fullStr The ‘damping effect’ in the dynamic response of stochastic oscillators
title_full_unstemmed The ‘damping effect’ in the dynamic response of stochastic oscillators
title_sort The ‘damping effect’ in the dynamic response of stochastic oscillators
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Sondipon Adhikari
author2 Sondipon Adhikari
Blanca Pascual
format Journal article
container_title Probabilistic Engineering Mechanics
container_volume 44
container_start_page 2
publishDate 2016
institution Swansea University
issn 0266-8920
doi_str_mv 10.1016/j.probengmech.2015.09.017
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 0
active_str 0
description We consider the dynamics of linear damped oscillators with stochastically perturbed natural frequencies. When average dynamic response is considered, it is observed that stochastic perturbation in the natural frequency manifests as an increase of the effective damping of the system. Assuming uniform distribution of the natural frequency, a closed-from expression of equivalent damping for the mean response has been derived to explain the ‘increasing damping’ behaviour. In addition to this qualitative analysis, a comprehensive quantitative analysis is proposed to calculate the statistics of frequency response functions from the probability density functions of the natural frequencies. Firstly, single-degree-of-freedom-systems are considered and closed-form analytical expressions for the mean and variance are obtained using a hybrid Laplace's method. Several probability density functions, including gamma, normal and lognormal distributions, are considered for the derivation of the analytical expressions. The method is extended to calculate the mean and the variance of the frequency response function of multiple-degrees-of-freedom dynamic systems. Proportional damping is assumed and the eigenvalues are considered to be independent. Results are derived for several probability density functions and damping factors. The accuracy of the approach for both single and multiple-degrees-of-freedom systems is examined using the direct Monte Carlo simulation.
published_date 2016-04-30T03:35:20Z
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score 11.012678

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