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Research Papers

Transfer Function Analysis of Constrained, Distributed Piezoelectric Vibration Energy Harvesting Beam Systems

[+] Author and Article Information
Chin An Tan

Professor
Department of Mechanical Engineering,
Wayne State University,
5050 Anthony Wayne Drive,
Detroit, MI 48202;
Sound and Vibration Laboratory,
College of Mechanical Engineering,
Zhejiang University of Technology,
18 Chaowang Road,
Hangzhou 310014, China
e-mail: tan@wayne.edu

Shahram Amoozegar

Department of Mechanical Engineering,
Wayne State University,
5050 Anthony Wayne Drive,
Detroit, MI 48202
e-mail: shahram.amoozegar@wayne.edu

Heather L. Lai

Mechanical Engineering,
Division of Engineering Programs SUNY,
New Paltz, NY 12561
e-mail: laih@engr.newpaltz.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 2, 2017; final manuscript received December 22, 2017; published online February 9, 2018. Assoc. Editor: Alper Erturk.

J. Vib. Acoust 140(3), 031015 (Feb 09, 2018) (15 pages) Paper No: VIB-17-1351; doi: 10.1115/1.4038949 History: Received August 02, 2017; Revised December 22, 2017

This paper presents a novel formulation and exact solution of the frequency response function (FRF) of vibration energy harvesting beam systems by the distributed transfer function method (TFM). The method is applicable for coupled electromechanical systems with nonproportional damping, intermediate constraints, and nonclassical boundary conditions, for which the system transfer functions are either very difficult or cumbersome to obtain using available methods. Such systems may offer new opportunities for optimized designs of energy harvesters via parameter tuning. The proposed formulation is also systematic and amenable to algorithmic numerical coding, allowing the system response and its derivatives to be computed by only simple modifications of the parameters in the system operators for different boundary conditions and the incorporation of feedback control principles. Examples of piezoelectric energy harvesters with nonclassical boundary conditions and intermediate constraints are presented to demonstrate the efficacy of the proposed method and its use as a design tool for vibration energy harvesters via tuning of system parameters. The results can also be used to provide benchmarks for assessing the accuracies of approximate techniques.

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Figures

Grahic Jump Location
Fig. 2

(a) Uncoupled FRF for undamped cantilever beam and (b) effect of additional terms in modal analysis on antiresonance modeling of undamped cantilever beam

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Fig. 1

Schematic of a unimorph vibration energy harvester under base excitations

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Fig. 3

Comparison between the TFM and the modal analysis solutions [42]: (a) voltage and (b) relative tip displacement

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Fig. 6

Cantilevered piezoelectric unimorph energy harvester with an intermediate rotational spring

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Fig. 4

Cantilevered piezoelectric unimorph energy harvester with a tip mass

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Fig. 5

Cantilevered piezoelectric unimorph energy harvester with nonideal clamped boundary conditions

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Fig. 7

Validation of the response of the piezoelectric unimorph beam energy harvester with a rotational spring against the result of the clamped-sliding beam

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Fig. 8

Validation of the piezoelectric unimorph beam energy harvester with rotational spring located at xr=L against the result of the cantilevered beam

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Fig. 9

Beam deflection FRF at xr=L for different values of Kr

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Fig. 10

Output voltage FRF at xr=L for different values of Kr

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