Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform

Qinghua Liu; Junyi Cao; Zehao Hou; Ying Zhang; Xingjian Jing

doi:10.1007/978-981-16-5912-6_43

Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform

Qinghua Liu
, Junyi Cao^*
, Zehao Hou
, Ying Zhang
, Xingjian Jing

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

1 Citation (Scopus)

Abstract

Nonlinear piezoelectric structures have attracted great attention in energy harvesting, vibration control, and morphing structures recently. The most important design and dynamic analysis parameters in a nonlinear piezoelectric structure is the nonlinear stiffness force. However, the nonlinear stiffness force is difficult to calculate analytically or measure statically under complicated practical engineering conditions. Therefore, this paper utilizes signal decomposition and the Hilbert transform-based method for the precise identification of stiffness force of a class of typical nonlinear piezoelectric structures. The quasi-zero stiffness, bistable stiffness, and tristable stiffness structures are designed in the magnetic coupled piezoelectric cantilever beam system. The identification process and the applicability based on free vibration and forced frequency-swept response for different nonlinear structures will be discussed. Numerical examples of quasi-zero stiffness, bistable stiffness, and tristable stiffness nonlinear piezoelectric structures show the necessity to choose the reasonable free decay and the forced frequency-swept response for accurate identification. In the experimental condition, the identified nonlinear stiffness force keeps in good agreement with the measurement by the dynamometer.

Original language	English
Title of host publication	Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021
Subtitle of host publication	The proceedings of 2021 International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC2021)
Editors	Xingjian Jing, Hu Ding, Jiqiang Wang
Place of Publication	Singapore
Publisher	Springer
Pages	584-596
ISBN (Electronic)	978-981-16-5912-6
ISBN (Print)	9789811659119, 978-981-16-5914-0
DOIs	https://doi.org/10.1007/978-981-16-5912-6_43
Publication status	Published - 2022
Externally published	Yes
Event	International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC-2021) - Hong Kong Polytechnic University, Hong Kong, China Duration: 23 Aug 2021 → 25 Aug 2021 http://www.icandvc.com/

Publication series

Name	Lecture Notes in Electrical Engineering
Volume	799
ISSN (Print)	1876-1100
ISSN (Electronic)	1876-1119

Conference

Conference	International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC-2021)
Abbreviated title	ICANDVC2021
Place	Hong Kong, China
Period	23/08/21 → 25/08/21
Internet address	http://www.icandvc.com/

Research Keywords

Hilbert transform
Nonlinear piezoelectric structures
Nonlinear stiffness force
Signal decomposition

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Liu, Q., Cao, J., Hou, Z., Zhang, Y., & Jing, X. (2022). Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform. In X. Jing, H. Ding, & J. Wang (Eds.), Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021: The proceedings of 2021 International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC2021) (pp. 584-596). (Lecture Notes in Electrical Engineering; Vol. 799). Springer . https://doi.org/10.1007/978-981-16-5912-6_43

Liu, Qinghua ; Cao, Junyi ; Hou, Zehao et al. / Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform. Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021: The proceedings of 2021 International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC2021). editor / Xingjian Jing ; Hu Ding ; Jiqiang Wang. Singapore : Springer , 2022. pp. 584-596 (Lecture Notes in Electrical Engineering).

@inproceedings{a3619f4f9c544440b6e924eb056e8640,

title = "Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform",

abstract = "Nonlinear piezoelectric structures have attracted great attention in energy harvesting, vibration control, and morphing structures recently. The most important design and dynamic analysis parameters in a nonlinear piezoelectric structure is the nonlinear stiffness force. However, the nonlinear stiffness force is difficult to calculate analytically or measure statically under complicated practical engineering conditions. Therefore, this paper utilizes signal decomposition and the Hilbert transform-based method for the precise identification of stiffness force of a class of typical nonlinear piezoelectric structures. The quasi-zero stiffness, bistable stiffness, and tristable stiffness structures are designed in the magnetic coupled piezoelectric cantilever beam system. The identification process and the applicability based on free vibration and forced frequency-swept response for different nonlinear structures will be discussed. Numerical examples of quasi-zero stiffness, bistable stiffness, and tristable stiffness nonlinear piezoelectric structures show the necessity to choose the reasonable free decay and the forced frequency-swept response for accurate identification. In the experimental condition, the identified nonlinear stiffness force keeps in good agreement with the measurement by the dynamometer.",

keywords = "Hilbert transform, Nonlinear piezoelectric structures, Nonlinear stiffness force, Signal decomposition",

author = "Qinghua Liu and Junyi Cao and Zehao Hou and Ying Zhang and Xingjian Jing",

year = "2022",

doi = "10.1007/978-981-16-5912-6\_43",

language = "English",

isbn = "9789811659119",

series = "Lecture Notes in Electrical Engineering",

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editor = "Xingjian Jing and Hu Ding and Jiqiang Wang",

booktitle = "Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021",

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Liu, Q, Cao, J, Hou, Z, Zhang, Y & Jing, X 2022, Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform. in X Jing, H Ding & J Wang (eds), Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021: The proceedings of 2021 International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC2021). Lecture Notes in Electrical Engineering, vol. 799, Springer , Singapore, pp. 584-596, International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC-2021), Hong Kong, China, 23/08/21. https://doi.org/10.1007/978-981-16-5912-6_43

Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform. / Liu, Qinghua; Cao, Junyi; Hou, Zehao et al.
Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021: The proceedings of 2021 International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC2021). ed. / Xingjian Jing; Hu Ding; Jiqiang Wang. Singapore: Springer , 2022. p. 584-596 (Lecture Notes in Electrical Engineering; Vol. 799).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform

AU - Liu, Qinghua

AU - Cao, Junyi

AU - Hou, Zehao

AU - Zhang, Ying

AU - Jing, Xingjian

PY - 2022

Y1 - 2022

N2 - Nonlinear piezoelectric structures have attracted great attention in energy harvesting, vibration control, and morphing structures recently. The most important design and dynamic analysis parameters in a nonlinear piezoelectric structure is the nonlinear stiffness force. However, the nonlinear stiffness force is difficult to calculate analytically or measure statically under complicated practical engineering conditions. Therefore, this paper utilizes signal decomposition and the Hilbert transform-based method for the precise identification of stiffness force of a class of typical nonlinear piezoelectric structures. The quasi-zero stiffness, bistable stiffness, and tristable stiffness structures are designed in the magnetic coupled piezoelectric cantilever beam system. The identification process and the applicability based on free vibration and forced frequency-swept response for different nonlinear structures will be discussed. Numerical examples of quasi-zero stiffness, bistable stiffness, and tristable stiffness nonlinear piezoelectric structures show the necessity to choose the reasonable free decay and the forced frequency-swept response for accurate identification. In the experimental condition, the identified nonlinear stiffness force keeps in good agreement with the measurement by the dynamometer.

AB - Nonlinear piezoelectric structures have attracted great attention in energy harvesting, vibration control, and morphing structures recently. The most important design and dynamic analysis parameters in a nonlinear piezoelectric structure is the nonlinear stiffness force. However, the nonlinear stiffness force is difficult to calculate analytically or measure statically under complicated practical engineering conditions. Therefore, this paper utilizes signal decomposition and the Hilbert transform-based method for the precise identification of stiffness force of a class of typical nonlinear piezoelectric structures. The quasi-zero stiffness, bistable stiffness, and tristable stiffness structures are designed in the magnetic coupled piezoelectric cantilever beam system. The identification process and the applicability based on free vibration and forced frequency-swept response for different nonlinear structures will be discussed. Numerical examples of quasi-zero stiffness, bistable stiffness, and tristable stiffness nonlinear piezoelectric structures show the necessity to choose the reasonable free decay and the forced frequency-swept response for accurate identification. In the experimental condition, the identified nonlinear stiffness force keeps in good agreement with the measurement by the dynamometer.

KW - Hilbert transform

KW - Nonlinear piezoelectric structures

KW - Nonlinear stiffness force

KW - Signal decomposition

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U2 - 10.1007/978-981-16-5912-6_43

DO - 10.1007/978-981-16-5912-6_43

M3 - RGC 32 - Refereed conference paper (with host publication)

AN - SCOPUS:85116485394

SN - 9789811659119

SN - 978-981-16-5914-0

T3 - Lecture Notes in Electrical Engineering

SP - 584

EP - 596

BT - Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021

A2 - Jing, Xingjian

A2 - Ding, Hu

A2 - Wang, Jiqiang

PB - Springer

CY - Singapore

T2 - International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC-2021)

Y2 - 23 August 2021 through 25 August 2021

ER -

Liu Q, Cao J, Hou Z, Zhang Y, Jing X. Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform. In Jing X, Ding H, Wang J, editors, Advances in Applied Nonlinear Dynamics, Vibration and Control - 2021: The proceedings of 2021 International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC2021). Singapore: Springer . 2022. p. 584-596. (Lecture Notes in Electrical Engineering). Epub 2021 Sept 24. doi: 10.1007/978-981-16-5912-6_43

Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform

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