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Research Papers

Multiple Mode Spatial Vibration Reduction in Flexible Beams Using H2- and H-Modified Positive Position Feedback

[+] Author and Article Information
Ehsan Omidi

Nonlinear Intelligent Structures Laboratory,
Department of Mechanical Engineering,
University of Alabama,
Tuscaloosa, AL 35487-0276
e-mail: eomidi@crimson.ua.edu

S. Nima Mahmoodi

Nonlinear Intelligent Structures Laboratory,
Department of Mechanical Engineering,
University of Alabama,
Tuscaloosa, AL 35487-0276
e-mail: nmahmoodi@eng.ua.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 March 4, 2014; final manuscript received May 30, 2014; published online November 12, 2014. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 137(1), 011016 (Feb 01, 2015) (7 pages) Paper No: VIB-14-1069; doi: 10.1115/1.4028011 History: Received March 04, 2014; Revised May 30, 2014; Online November 12, 2014

This paper develops H2 modified positive position feedback (H2-MPPF) and H-MPPF controllers for spatial vibration suppression of flexible structures in multimode condition. Resonant vibrations in a clamped–clamped (c–c) and a cantilever beam are aimed to be spatially suppressed using minimum number of piezoelectric patches. These two types of beams are selected since they are more frequently used in macro- and microscale structures. The shape functions of the beams are extracted using the assumed-modes approach. Then, they are implemented in the controller design via spatial H2 and H norms. The controllers are then evaluated experimentally. Vibrations of multiple points on the beams are concurrently measured using a laser vibrometer. According to the results of the c–c beam, vibration amplitude is reduced to less than half for the entire beam using both H2- and H-MPPF controllers. For the cantilever beam, vibration amplitude is suppressed to a higher level using the H2-MPPF controller compared to the H-MPPF method. Results show that the designed controllers can effectively use one piezoelectric actuator to efficiently perform spatial vibration control on the entire length of the beams with different boundary conditions.

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References

Figures

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Fig. 7

Spatial FFT plot of the uncontrolled cantilever beam (ref: 0 dB, 1 m/s)

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Fig. 9

Piezo-input voltage for spatial multimode H2- and H-MPPF vibration suppression of the cantilever beam

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Fig. 2

Measurement points: (a) c–c beam and (b) cantilever beam

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Fig. 3

Velocity amplitude of the controlled and uncontrolled c–c beam: (a) spatial multimode H2-MPPF controller and (b) spatial multimode H-MPPF controller

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Fig. 4

FFT plot of the uncontrolled c–c beam (ref: 0 dB, 1 m/s)

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Fig. 5

FFT plot of the controlled c–c beam (ref: 0 dB, 1 m/s): (a) spatial multimode H2-MPPF controller and (b) spatial multimode H-MPPF controller

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Fig. 6

Vibration amplitude of the controlled and uncontrolled cantilever beam: (a) spatial multimode H2-MPPF controller and (b) spatial multimode H-MPPF controller

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Fig. 1

Schematic view of a c–c beam with attached piezoelectric actuators and sensors

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Fig. 8

FFT plot of the controlled c–c beam (ref: 0 dB, 1 m/s): (a) spatial multimode H2-MPPF controller and (b) spatial multimode H-MPPF controller

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