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Research Papers

Nonparametric Identification of Nonlinear Piezoelectric Mechanical Systems

[+] Author and Article Information
Tian-Chen Yuan

Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China

Jian Yang

School of Urban Railway Transportation,
Shanghai University of Engineering Science,
Shanghai 201620, China

Li-Qun Chen

Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China;
Department of Mechanics,
Shanghai University,
99 Shang Da Road,
Shanghai 200444, China;
Shanghai Key Laboratory of Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: lqchen@staff.shu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 10, 2018; final manuscript received July 15, 2018; published online August 24, 2018. Assoc. Editor: George Haller.

J. Appl. Mech 85(11), 111008 (Aug 24, 2018) (13 pages) Paper No: JAM-18-1141; doi: 10.1115/1.4040949 History: Received March 10, 2018; Revised July 15, 2018

Two novel nonparametric identification approaches are proposed for piezoelectric mechanical systems. The novelty of the approaches is using not only mechanical signals but also electric signals. The expressions for unknown mechanical and electric terms are given based on the Hilbert transform. The signals are decomposed and re-assembled to obtain smooth stiffness and damping curves. The current mapping approach is developed to identify accurately a piezoelectric mechanical system with strongly nonlinear electric terms. The developed identification approaches are successfully implemented to simulate signals obtained from different nonlinear piezoelectric mechanical systems, including Duffing nonlinearity, softening and hardening nonlinearity, and Duffing nonlinearity with strong nonlinear electric terms. The proposed approaches are successfully applied to experimental signals of a circular laminated plate device in order to identify the nonlinear stiffness functions, damping functions, electromechanical coupling functions, and equivalent capacitance functions. The results show both softening and hardening nonlinearity in the stiffness characteristic and weak nonlinearity in electric characteristics. The results of the Hilbert transform based approach and the current mapping approach are compared, and the outcomes show good agreements.

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Figures

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Fig. 1

The schematic diagram of separation

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Fig. 2

Displacement (a) and voltage (b) responses of the Duffing system

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Fig. 3

Identification results of the Duffing system: stiffness (a), damping (b), electromechanical coupling (c), and equivalent capacitance (d)

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Fig. 16

Identification results of the piezoelectric harvester: stiffness (a) and damping (b)

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Fig. 15

The three-dimensional plot of the IF and the envelope of the piezoelectric harvester (ds = 49 mm): displacement (a) and voltage (b)

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Fig. 14

The three-dimensional plot of the IF and the envelope of the piezoelectric harvester (ds = 56 mm): displacement (a) and voltage (b)

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Fig. 13

Displacement (a) and voltage (b) responses of the piezoelectric harvester (ds = 49 mm)

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Fig. 12

Displacement (a) and voltage (b) responses of the piezoelectric harvester (ds = 56 mm)

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Fig. 11

Cutaway view of the laminated piezoelectric plate harvester

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Fig. 10

Identification results compared to the accurate results: electromechanical coupling (a) and equivalent capacitance (b)

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Fig. 9

Identification results: electromechanical coupling (a) and equivalent capacitance (b)

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Fig. 8

The velocity–current curve (a) and the derivative of voltage–current curve (b)

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Fig. 7

The current surface of the system with nonlinear electric terms

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Fig. 6

Identification results of the system with nonlinear electric terms: stiffness (a) and damping (b)

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Fig. 5

Identification results of the system with softening and hardening nonlinearity: stiffness (a), damping (b), electromechanical coupling (c), and equivalent capacitance (d)

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Fig. 4

Displacement (a) and voltage (b) responses of the system with softening and hardening nonlinearity

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Fig. 17

The velocity–current curve (a) and derivative of voltage–current curve (b) of the piezoelectric harvester (ds = 56 mm)

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Fig. 18

The velocity–current curve (a) and derivative of voltage–current curve (b) of the piezoelectric harvester (ds = 49 mm)

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Fig. 19

Identification results of the piezoelectric harvester (ds = 56 mm): electromechanical coupling (a) and equivalent capacitance (b)

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Fig. 20

Identification results of the piezoelectric harvester (ds = 49 mm): electromechanical coupling (a) and equivalent capacitance (b)

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Fig. 21

The effect of voltage on the identification results: (a) stiffness and (b) damping

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