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Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force

Javad Taghipour, Hamed Haddad Khodaparast Orcid Logo, Michael Friswell, Alexander Shaw Orcid Logo, Hassan Jalali, Nidhal Jamia Orcid Logo

Mechanical Systems and Signal Processing, Volume: 162, Start page: 108057

Swansea University Authors: Javad Taghipour, Hamed Haddad Khodaparast Orcid Logo, Michael Friswell, Alexander Shaw Orcid Logo, Nidhal Jamia Orcid Logo

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DOI (Published version): 10.1016/j.ymssp.2021.108057

Abstract

Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and r...

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Published in: Mechanical Systems and Signal Processing
ISSN: 0888-3270
Published: Elsevier BV 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa56936
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Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. 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spelling 2022-08-16T14:36:36.7588885 v2 56936 2021-05-21 Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force dc7cba835218dde37fe7f447962d4058 Javad Taghipour Javad Taghipour true false f207b17edda9c4c3ea074cbb7555efc1 0000-0002-3721-4980 Hamed Haddad Khodaparast Hamed Haddad Khodaparast true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 846b2cd3a7717b296654010df30cb22a 0000-0003-0643-7812 Nidhal Jamia Nidhal Jamia true false 2021-05-21 Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated. Journal Article Mechanical Systems and Signal Processing 162 108057 Elsevier BV 0888-3270 Structural dynamics, Nonlinear identification, Multi-harmonic response, Harmonic balance 1 1 2022 2022-01-01 10.1016/j.ymssp.2021.108057 COLLEGE NANME COLLEGE CODE Swansea University External research funder(s) paid the OA fee (includes OA grants disbursed by the Library) The authors acknowledge the financial support from the Engineering and Physical Sciences Research Council, through grant numbers EP/R006768/1, EP/S017925/1 and EP/P01271X/1. Javad Taghipour gratefully acknowledges the financial support from the College of Engineering at Swansea University. 2022-08-16T14:36:36.7588885 2021-05-21T09:50:53.5202294 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Javad Taghipour 1 Hamed Haddad Khodaparast 0000-0002-3721-4980 2 Michael Friswell 3 Alexander Shaw 0000-0002-7521-827X 4 Hassan Jalali 5 Nidhal Jamia 0000-0003-0643-7812 6 56936__20019__28f0c68dd6354ec78850a20a8de57d86.pdf 56936.pdf 2021-05-28T08:53:01.1755987 Output 7591981 application/pdf Version of Record true © 2021 The Authors. This is an open access article under the CC BY license true eng http://creativecommons.org/licenses/by/4.0/
title Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force
spellingShingle Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force
Javad Taghipour
Hamed Haddad Khodaparast
Michael Friswell
Alexander Shaw
Nidhal Jamia
title_short Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force
title_full Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force
title_fullStr Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force
title_full_unstemmed Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force
title_sort Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force
author_id_str_mv dc7cba835218dde37fe7f447962d4058
f207b17edda9c4c3ea074cbb7555efc1
5894777b8f9c6e64bde3568d68078d40
10cb5f545bc146fba9a542a1d85f2dea
846b2cd3a7717b296654010df30cb22a
author_id_fullname_str_mv dc7cba835218dde37fe7f447962d4058_***_Javad Taghipour
f207b17edda9c4c3ea074cbb7555efc1_***_Hamed Haddad Khodaparast
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
10cb5f545bc146fba9a542a1d85f2dea_***_Alexander Shaw
846b2cd3a7717b296654010df30cb22a_***_Nidhal Jamia
author Javad Taghipour
Hamed Haddad Khodaparast
Michael Friswell
Alexander Shaw
Nidhal Jamia
author2 Javad Taghipour
Hamed Haddad Khodaparast
Michael Friswell
Alexander Shaw
Hassan Jalali
Nidhal Jamia
format Journal article
container_title Mechanical Systems and Signal Processing
container_volume 162
container_start_page 108057
publishDate 2022
institution Swansea University
issn 0888-3270
doi_str_mv 10.1016/j.ymssp.2021.108057
publisher Elsevier BV
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
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description Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated.
published_date 2022-01-01T05:05:48Z
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