Research Papers

Analytical and Finite Element Modal Analysis of a Hyperelastic Membrane for Micro Air Vehicle Wings

[+] Author and Article Information
Uttam Kumar Chakravarty

Department of Mechanical Engineering,
University of New Orleans,
New Orleans, LA 70148
e-mail: uchakrav@uno.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 2, 2011; final manuscript received April 7, 2013; published online June 18, 2013. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 135(5), 051004 (Jun 18, 2013) (6 pages) Paper No: VIB-11-1126; doi: 10.1115/1.4024213 History: Received June 02, 2011; Revised April 07, 2013

Analytical and finite element models are developed for investigating the modal characteristics of a hyperelastic rubber latex membrane for micro air vehicle wings applications. A radially prestretched membrane specimen is attached to a thin, rigid circular ring and vibrated in vacuum and in air at atmospheric pressure. The natural frequencies of the membrane computed by analytical and finite element models are correlated well. The natural frequencies increase with mode and prestretch level of the membrane but decrease in air from those in vacuum due to the effect of added mass of air. The damping is low and has a very minimal effect on the frequencies but helps to reduce the amplitude of vibration. Aerodynamic pressure at different angles of attack and a freestream velocity is computed from the wind tunnel test data, and a finite element model is developed for investigating the effect of the aerodynamic pressure on the modal characteristics of the membrane. It is found that the effect of aerodynamic pressure on the natural frequencies of the membrane is not significant.

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Fig. 1

Two MAVs from the MAV Lab at the University of Florida, Gainesville, FL

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Fig. 2

(a) Initial (stretch free) and (b) prestretched configurations of the circular membrane specimen. O (0,0) is the center of the membrane specimen.

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Fig. 3

Natural frequencies (fmn = ωmn/2π) versus prestretch ratio plots for the membrane specimen in vacuum

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Fig. 4

Natural frequencies versus prestretch ratio plots for the membrane specimen in air

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Fig. 5

Mode shapes of the membrane specimen in air: (a) first (0, 1) mode shape, (b) second (1, 1) mode shape, (c) third (2, 1) mode shape

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Fig. 6

Coefficient of lift versus angle of attack plot at V = 13.0 m/s

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Fig. 7

Aerodynamic pressure versus angle of attack plot at V = 13.0 m/s

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Fig. 8

Static out-of-plane deformation of the membrane specimen at α = 20 deg and V = 13.0 m/s

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Fig. 9

Variation of static out-of-plane deformation at the center of the membrane specimen with aerodynamic pressure at V = 13.0 m/s

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Fig. 10

Mode shapes of the membrane specimen at α = 20 deg and V = 13.0 m/s: (a) first (0, 1) mode shape, (b) second (1, 1) mode shape, and (c) third (2, 1) mode shape




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