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Research Papers

Analytical Solutions to H2 and H Optimizations of Resonant Shunted Electromagnetic Tuned Mass Damper and Vibration Energy Harvester

[+] Author and Article Information
Xiudong Tang, Wen Cui

Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794

Yilun Liu

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

Lei Zuo

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061;
Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794
e-mail: leizuo@vt.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 February 1, 2014; final manuscript received October 7, 2015; published online November 23, 2015. Assoc. Editor: Jiong Tang.

J. Vib. Acoust 138(1), 011018 (Nov 23, 2015) (8 pages) Paper No: VIB-14-1034; doi: 10.1115/1.4031823 History: Received February 01, 2014; Revised October 07, 2015

When optimized, tuned mass dampers (TMDs) can effectively mitigate the vibration of the primary structure, because additional resonance and damping are introduced by the auxiliary mass-spring-damper system. Similar effect can be realized without auxiliary mass when an electromagnetic transducer shunt with the R-L-C resonant circuit is placed between the primary structure and the base. This paper is to analytically optimize the parameters of the R-L-C circuits for vibration mitigation. Both H2 and H optimization criteria are investigated, which are to minimize the root-mean-square (RMS) vibration under random excitation and the peak magnitude in the frequency domain, respectively. The concise closed-form solutions of the optimal parameters are then summarized together with the ones obtained the using fixed-point method, for practical implementation convenience. The H2 and H optimizations of energy harvesting are also discussed in this paper. Furthermore, we also investigate the sensitivity of system performances to the tuning parameter changes of the electromagnetic shunt circuit.

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Figures

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Fig. 1

(a) Classic TMD, (b) electromagnetic TMD or vibration energy harvester shunted with an R-L-C circuit, and (c) a traditional electromagnetic vibration harvester with a resistive charging circuit

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Fig. 2

The frequency responses of the classic TMD of mass ratio μ=1% and electromagnetic shunt TMD of stiffness ratio μk= 1%

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Fig. 3

Sensitivity of vibration suppression of the H2 optimal electromagnetic shunt TMD to changes of the tuning parameters regarding H2 performance index

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Fig. 4

Sensitivity of vibration suppression of the H2 optimal electromagnetic shunt TMD to 5% changes of the tuning circuit parameters

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Fig. 5

Sensitivity of vibration suppression of the H2 optimal electromagnetic shunt TMD to the parameter changes of the primary systems

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Fig. 6

Frequency responses of the energy harvesting power of electromagnetic TMD with resonant circuit and with resistive load, where stiffness ratio μk= 1%, frequency tuning ratio f = 0.95, and damping ζe= 2%

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Fig. 7

The impulse response of the dimensionless electromagnetic shunt TMD systems optimized by H2, H∞, and fixed-point methods

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