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An extended harmonic balance method based on incremental nonlinear control parameters

Hamed Haddad Khodaparast Orcid Logo, Hadi Madinei Orcid Logo, Michael Friswell, Sondipon Adhikari, Simon Coggon, Jonathan E. Cooper

Mechanical Systems and Signal Processing, Volume: 85, Pages: 716 - 729

Swansea University Authors: Hamed Haddad Khodaparast Orcid Logo, Hadi Madinei Orcid Logo, Michael Friswell, Sondipon Adhikari

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DOI (Published version): 10.1016/j.ymssp.2016.09.008

Abstract

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of ‘non-li...

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Published in: Mechanical Systems and Signal Processing
ISSN: 0888-3270
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa29776
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spelling 2020-07-17T14:40:06.0784367 v2 29776 2016-09-07 An extended harmonic balance method based on incremental nonlinear control parameters f207b17edda9c4c3ea074cbb7555efc1 0000-0002-3721-4980 Hamed Haddad Khodaparast Hamed Haddad Khodaparast true false d9a10856ae9e6a71793eab2365cff8b6 0000-0002-3401-1467 Hadi Madinei Hadi Madinei true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2016-09-07 AERO A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of ‘non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices. Journal Article Mechanical Systems and Signal Processing 85 716 729 0888-3270 15 2 2017 2017-02-15 10.1016/j.ymssp.2016.09.008 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2020-07-17T14:40:06.0784367 2016-09-07T11:30:00.5171572 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Hamed Haddad Khodaparast 0000-0002-3721-4980 1 Hadi Madinei 0000-0002-3401-1467 2 Michael Friswell 3 Sondipon Adhikari 4 Simon Coggon 5 Jonathan E. Cooper 6 0029776-07092016113107.pdf khodaparast2016.pdf 2016-09-07T11:31:07.2870000 Output 1712232 application/pdf Accepted Manuscript true 2017-09-17T00:00:00.0000000 true
title An extended harmonic balance method based on incremental nonlinear control parameters
spellingShingle An extended harmonic balance method based on incremental nonlinear control parameters
Hamed Haddad Khodaparast
Hadi Madinei
Michael Friswell
Sondipon Adhikari
title_short An extended harmonic balance method based on incremental nonlinear control parameters
title_full An extended harmonic balance method based on incremental nonlinear control parameters
title_fullStr An extended harmonic balance method based on incremental nonlinear control parameters
title_full_unstemmed An extended harmonic balance method based on incremental nonlinear control parameters
title_sort An extended harmonic balance method based on incremental nonlinear control parameters
author_id_str_mv f207b17edda9c4c3ea074cbb7555efc1
d9a10856ae9e6a71793eab2365cff8b6
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4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv f207b17edda9c4c3ea074cbb7555efc1_***_Hamed Haddad Khodaparast
d9a10856ae9e6a71793eab2365cff8b6_***_Hadi Madinei
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Hamed Haddad Khodaparast
Hadi Madinei
Michael Friswell
Sondipon Adhikari
author2 Hamed Haddad Khodaparast
Hadi Madinei
Michael Friswell
Sondipon Adhikari
Simon Coggon
Jonathan E. Cooper
format Journal article
container_title Mechanical Systems and Signal Processing
container_volume 85
container_start_page 716
publishDate 2017
institution Swansea University
issn 0888-3270
doi_str_mv 10.1016/j.ymssp.2016.09.008
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 1
active_str 0
description A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of ‘non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
published_date 2017-02-15T03:36:16Z
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score 11.013731

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