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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Den Hartog, J. P. , 1947, Mechanical Vibration, McGraw-Hill, New York.
Xu, K. , and Igusa, T. , 1992, “ Dynamic Characteristics of Multiple Substructures With Closely Spaced Frequencies,” Earthquake Eng. Struct. Dyn., 21(12), pp. 1059–1070. [CrossRef]
Yamaguchi, H. , and Hampornchai, N. , 1993, “ Fundamental Characteristics of Multiple Tuned Mass Dampers for Suppressing Harmonically Forced Oscillations,” Earthquake Eng. Struct. Dyn., 22(1), pp. 51–62. [CrossRef]
Zuo, L. , and Nayfeh, S. , 2002, “ Design of Multi-Degree-of-Freedom Tuned-Mass Dampers: A Minimax Approach,” AIAA Paper No. 2002-1283.
Snowdon, J. , 1974, “ Dynamic Vibration Absorbers That Have Increased Effectiveness,” ASME J. Eng. Ind., 96(3), pp. 940–945. [CrossRef]
Zuo, L. , 2009, “ Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers,” ASME J. Vib. Acoust., 131(3), p. 031003. [CrossRef]
Warburton, G. , 1982, “ Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters,” Earthquake Eng. Struct. Dyn., 10(3), pp. 381–401. [CrossRef]
Asami, T. , Nishihara, O. , and Baz, A. M. , 2002, “ Analytical Solutions to H and H2 Optimization of Dynamic Vibration Absorber Attached to Damped Linear Systems,” ASME J. Vib. Acoust., 124(2), pp. 67–78.
Forward, R. L. , 1979, “ Electronic Damping of Vibrations in Optical Structures,” Appl. Opt., 18(5), pp. 690–697. [CrossRef] [PubMed]
Hagood, N. W. , and von Flotow, A. , 1991, “ Damping of Structural Vibrations With Piezoelectric Materials and Passive Electrical Networks,” J. Sound Vib., 146(2), pp. 243–268. [CrossRef]
Moheimani, S. O. R. , 2003, “ A Survey of Recent Innovations in Vibration Damping and Control Using Shunted Piezoelectric Transducers,” IEEE Trans. Control Syst. Technol., 11(4), pp. 482–494. [CrossRef]
Lesieutre, G. A. , 1998, “ Vibration Damping and Control Using Shunted Piezoelectric Materials,” Shock Vib. Dig., 30(3), pp. 187–195. [CrossRef]
Behrens, S. , Fleming, A. J. , and Moheimani, S. , 2003, “ Electromagnetic Shunt Damping,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2003), Kobe, Japan, July 20–24, pp. 1145–1150.
Behrens, S. , Fleming, A. J. , and Moheimani, S. , 2003, “ Passive Vibration Control Via Electromagnetic Shunt Damping,” IEEE/ASME Trans. Mechatron., 10(1), pp. 118–122. [CrossRef]
Inoue, T. , Ishida, Y. , and Sumi, M. , 2008, “ Vibration Suppression Using Electromagnetic Resonant Shunt Damper,” ASME J. Vib. Acoust., 130(4), p. 041003. [CrossRef]
Zuo, L. , and Cui, W. , 2013, “ Dual-Functional Energy-Harvesting and Vibration Control: Electromagnetic Resonant Shunt Series Tuned Mass Dampers,” ASME J. Vib. Acoust., 135(5), pp. 510181–510189. [CrossRef]
Lefeuvre, E. , Audigier, D. , Richard, C. , and Guyomar, D. , 2007, “ Buck-Boost Converter for Sensorless Power Optimization of Piezoelectric Energy Harvester,” IEEE Trans. Power Electron., 22(5), pp. 2018–2025. [CrossRef]
Zhou, K. , Doyle, J. C. , and Glover, K. , 1995, Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, NJ.
Gradshtenyn, I. S. , and Ryzhik, I. M. , 1994, Table of Integrals Series, and Products, Academic Press, Boston.
Tang, X. , and Zuo, L. , 2012, “ Vibration Energy Harvesting From Random Force and Motion Excitations,” Smart Mater. Struct., 21(7), p. 075025. [CrossRef]
Nishihara, O. , and Asami, T. , 2002, “ Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers,” ASME J. Vib. Acoust., 124(4), pp. 576–582. [CrossRef]
Tang, X. , and Zuo, L. , 2011, “ Enhanced Vibration Energy Harvesting Using Dual-Mass Systems,” J. Sound Vib., 330(21), pp. 5199–5209. [CrossRef]
Stephen, N. G. , 2006, “ On Energy Harvesting From Ambient Vibration,” J. Sound Vib., 293(1–2), pp. 409–425. [CrossRef]


Grahic Jump Location
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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
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%

Grahic Jump Location
Fig. 7

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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In