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Research Papers

Precision Microscopic Actuations of Parabolic Cylindrical Shell Reflectors

[+] Author and Article Information
S. D. Hu, H. Li

StrucTronics and Control Lab,
School of Aeronautics and Astronautics,
Zhejiang University,
Hangzhou 310027, China

H. S. Tzou

School of Aeronautics and Astronautics,
Zhejiang University
The State Key Laboratory of
Fluid Power Transmission and Control,
Department of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: hstzou@zju.edu.cn

1Current address: Advanced Technologies Institute, Ningbo University.

2Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 30, 2014; final manuscript received June 24, 2014; published online November 12, 2014. Assoc. Editor: Ryan L. Harne.

J. Vib. Acoust 137(1), 011013 (Feb 01, 2015) (11 pages) Paper No: VIB-14-1108; doi: 10.1115/1.4028341 History: Received March 30, 2014; Revised June 24, 2014; Online November 12, 2014

An open parabolic cylindrical shell panel plays a key role in radial signal collection, reflection, and/or transmission applied to radar antennas, space reflectors, solar collectors, etc. Active vibration control can suppress unexpected fluctuation and maintain its precision surface and operations. This study aims to investigate the distributed active actuation behavior of adaptive open parabolic cylindrical shell panels using piezoelectric actuator patches. Dynamic equations of parabolic cylindrical shells laminated with piezoelectric actuator patches are presented first. Then, the actuator induced modal control force is defined based on a newly derived mode shape function. As the actuator area varies due to the curvature change, the normalized actuation effectiveness (i.e., modal control force per unit actuator area) is further evaluated. When the actuator area shrinks to infinitesimal, the expression of microscopic local modal control force is obtained to predict the spatial microscopic actuation behavior on parabolic cylindrical shells. The total control force and its three components exhibit distinct characteristics with respect to shell geometries, modes, and actuator properties. Analyzes suggest that the control force contributed by the membrane force component dominates the total actuation effect. The bending-contributed component increases with the corresponding mode number, while the membrane-contributed component decreases. Actuation effectiveness of two shell geometries, from shallow to deep, and actuator sizes are evaluated. Analysis of optimal actuator locations reveals that actuators placed at the maximal shell curvature are more effective and maximize the control effects.

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References

Figures

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Fig. 1

A parabolic cylindrical shell panel with an actuator patch: (a) perspective view and (b) left-half of the front view

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Fig. 2

Spatial distributions of microscopic actuation effectiveness of shallow panels, mode (1,1)

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Fig. 3

Spatial distributions of microscopic actuation effectiveness of shallow panels, mode (1,2)

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Fig. 11

Distributed actuation effectiveness of 40 segments: (a) the (m,1) mode, (b) the (m,2) mode, (c) the (m,3) mode, and (d) the (m,4) mode

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Fig. 12

Distributed actuation effectiveness of 20 segments: (a) the (m,1) mode, (b) the (m,2) mode, (c) the (m,3) mode, and (d) the (m,4) mode

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Fig. 14

Maximal actuation effectiveness versus actuator segmentation

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Fig. 6

Spatial distributions of microscopic actuation effectiveness of deep panels, mode (1,1)

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Fig. 7

Spatial distributions of microscopic actuation effectiveness of deep panels, mode (1,2)

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Fig. 8

Spatial distributions of microscopic actuation effectiveness of deep panels, mode (2,1)

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Fig. 9

Spatial distributions of microscopic actuation effectiveness of deep panels, mode (2,2)

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Fig. 4

Spatial distributions of microscopic actuation effectiveness of shallow panels, (2,1)

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Fig. 5

Spatial distributions of microscopic actuation effectiveness of shallow panels, (2,2)

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Fig. 10

Distributed segmented actuator patches

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Fig. 13

Distributed actuation effectiveness of ten segments: (a) the (m,1) mode, (b) the (m,2) mode, (c) the (m,3) mode, and (d) the (m,4) mode

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