Research Papers

Switch Triggers for Optimal Vibration Reduction Via Resonance Frequency Detuning

[+] Author and Article Information
Garrett K. Lopp

Department of Mechanical and
Aerospace Engineering,
University of Central Florida,
Orlando, FL 32816
e-mail: GLopp8590@knights.ucf.edu

Jeffrey L. Kauffman

Department of Mechanical and
Aerospace Engineering,
University of Central Florida,
Orlando, FL 32816
e-mail: JLKauffman@ucf.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 29, 2014; final manuscript received August 24, 2015; published online October 15, 2015. Editor: I. Y. (Steve) Shen.

J. Vib. Acoust 138(1), 011002 (Oct 15, 2015) (8 pages) Paper No: VIB-14-1323; doi: 10.1115/1.4031517 History: Received August 29, 2014; Revised August 24, 2015

Resonance frequency detuning (RFD) reduces vibration of systems subjected to frequency sweep excitation by altering the structural stiffness state as the excitation frequency passes through resonance. This vibration reduction technique applies to turbomachinery experiencing changes in rotation speed, for example, on spool-up and spool-down, and can be achieved through the inclusion of piezoelectric material and manipulation of its electrical boundary conditions. Key system parameters—the excitation sweep rate, modal damping ratio, electromechanical coupling coefficient, and, most importantly, the switch trigger that initiates the stiffness state switch (represented here in terms of excitation frequency)—determine the peak response dynamics. This paper exploits an analytical solution to a nondimensional single degree-of-freedom equation of motion to provide this blade response and recasts the equation in scaled form to include the altered system dynamics following the stiffness state switch. An extensive study over a range of sweep rates, damping ratios, and electromechanical coupling coefficients reveals the optimal frequency switch trigger that minimizes the peak of the blade response envelope. This switch trigger is primarily a function of the electromechanical coupling coefficient and the phase of vibration at which the switch occurs. As the coupling coefficient increases, the frequency-based switch trigger decreases, approximately linearly with the square of the coupling coefficient. Furthermore, as with other state-switching techniques, the optimal stiffness switch occurs on peak strain energy; however, the degradation in vibration reduction performance associated with a switch occurring at a nonoptimal phase is negligible for slow sweep rates and low modal damping.

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


El-Aini, Y. , deLaneuville, R. , Stoner, A. , and Capece, V. , 1997, “ High Cycle Fatigue of Turbomachinery Components—Industry Perspective,” AIAA Paper No. 97-3365.
Kauffman, J. L. , and Lesieutre, G. A. , 2012, “ Piezoelectric-Based Vibration Reduction of Turbomachinery Bladed Disks Via Resonance Frequency Detuning,” AIAA J., 50(5), pp. 1137–1144. [CrossRef]
Damjanovic, D. , 1998, “ Materials for High Temperature Piezoelectric Transducers,” Curr. Opin. Solid State Mater. Sci., 3(5), pp. 469–473. [CrossRef]
Zhang, S. , Xia, R. , Lebrun, L. , Anderson, D. , and Shrout, T. R. , 2005, “ Piezoelectric Materials for High Power, High Temperature Applications,” Mater. Lett., 59(27), pp. 3471–3475. [CrossRef]
Amoo, L. M. , 2013, “ On the Design and Structural Analysis of Jet Engine Fan Blade Structures,” Prog. Aerosp. Sci., 60, pp. 1–11. [CrossRef]
Lin, Y. , and Sodano, H. A. , 2009, “ Fabrication and Electromechanical Characterization of a Piezoelectric Structural Fiber for Multifunctional Composites,” Adv. Funct. Mater., 19(4), pp. 592–598. [CrossRef]
IEEE, 1988, “IEEE Standard on Piezoelectricity,” Institute of Electrical and Electronics Engineers, New York, Standard No. ANSI/IEEE 176-1987.
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]
Thomas, O. , Ducarne, J. , and Deu, J.-F. , 2012, “ Performance of Piezoelectric Shunts for Vibration Reduction,” Smart Mater. Struct., 21(1), p. 015008. [CrossRef]
Wu, S.-Y. , 1998, “ Method for Multiple Mode Piezoelectric Shunting with Single PZT Transducer for Vibration Control,” J. Intell.Mat. Syst. Struct., 9(12), pp. 991–998. [CrossRef]
Behrens, S. , and Moheimani, S. O. R. , 2002, “ Current Flowing Multiple-Mode Piezoelectric Shunt Dampener,” Proc. SPIE, 4697, pp. 217–226.
Clark, W. W. , 2000, “ Vibration Control With State-Switched Piezoelectric Materials,” J. Intell. Mater. Syst. Struct., 11(4), pp. 263–271. [CrossRef]
Richard, C. , Guyomar, D. , Audigier, D. , and Ching, G. , 1999, “ Semi-Passive Damping Using Continuous Switching of a Piezoelectric Device,” Proc. SPIE, 3672, pp. 104–111.
Richard, C. , Guyomar, D. , Audigier, D. , and Bassaler, H. , 2000, “ Enhanced Semi-Passive Damping Using Continuous Switching of a Piezoelectric Device on an Inductor,” Proc. SPIE, 3989, pp. 288–299.
Lefeuvre, E. , Badel, A. , Petit, L. , Richard, C. , and Guyomar, D. , 2006, “ Semi-Passive Piezoelectric Structural Damping by Synchronized Switching on Voltage Sources,” J. Intell. Mater. Syst. Struct., 17(8–9), pp. 653–660. [CrossRef]
Niederberger, D. , and Morari, M. , 2006, “ An Autonomous Shunt Circuit for Vibration Damping,” Smart Mater. Struct., 15(2), pp. 359–364. [CrossRef]
Lallart, M. , Lefeuvre, E. , Richard, C. , and Guyomar, D. , 2008, “ Self-Powered Circuit for Broadband, Multimodal Piezoelectric Vibration Control,” Sens. Actuators, A, 143(2), pp. 377–382. [CrossRef]
Kauffman, J. L. , and Lesieutre, G. A. , 2009, “ A Low-Order Model for the Design of Piezoelectric Energy Harvesting Devices,” J. Intell. Mater. Syst. Struct., 20(5), pp. 495–504. [CrossRef]
Korakianitis, T. , 1993, “ Influence of Stator-Rotor Gap on Axial-Turbine Unsteady Forcing Functions,” AIAA J., 31(7), pp. 1256–1264. [CrossRef]
Markert, R. , and Seidler, M. , 2001, “ Analytically Based Estimation of the Maximum Amplitude During Passage Through Resonance,” Int. J. Solids Struct., 38(10–13), pp. 1975–1992. [CrossRef]
Kosmatka, J. B. , and Mehmed, O. , 1998, “ Vibrational Reduction in Integral Damped Composite Fan Blades: Experimental Results,” Proc. SPIE, 3327, pp. 115–127.


Grahic Jump Location
Fig. 1

Structural resonance frequencies (solid lines) and excitation (dashed lines) versus rotation speed (from Ref. [2])

Grahic Jump Location
Fig. 2

Detuning of structural stiffness from 2S1 to 2S0 near 3950 rpm crossing (from Ref. [2])

Grahic Jump Location
Fig. 3

Response envelope for harmonic and swept-frequency excitation for ζ=0.5% and α=3×10−4 with end time τ=1.5/α=5000

Grahic Jump Location
Fig. 4

Response envelope for baseline system and detuned at ωsw=0.96 for ζ=0.5%, α=3×10−4, and k2=10%

Grahic Jump Location
Fig. 5

Frequency domain representation of the open-circuit and short-circuit responses with the optimal response shown

Grahic Jump Location
Fig. 6

Response envelopes for arbitrary switch triggers and open- and short-circuit cases, for α=10−4, ζ=0.1%, and k2=5%

Grahic Jump Location
Fig. 7

The peaks of each response (dots in Fig. 6) mapped to their frequency-based switch triggers, with optimal trigger value (circle)

Grahic Jump Location
Fig. 8

Optimal trigger versus sweep rate

Grahic Jump Location
Fig. 9

Optimal trigger versus coupling coefficient for ωsw applied at peak strain energy and peak kinetic energy, and optimal trigger values from Eq. (25)

Grahic Jump Location
Fig. 10

Normalized peak response versus switch trigger for ωsw applied at peak strain energy and peak kinetic energy for α=10−4, ζ=0.01%, and k2=20%

Grahic Jump Location
Fig. 11

Degradation in vibration reduction for ωsw* applied at peak kinetic energy compared to peak strain energy



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