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.

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Fig. 1

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

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Fig. 2

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

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Fig. 6

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

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Fig. 7

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

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Fig. 11

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

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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%

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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)

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Fig. 8

Optimal trigger versus sweep rate

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Fig. 5

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

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Fig. 4

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

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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




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