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Nonlinear aerodynamic damping of sharp-edged flexible beams oscillating at low Keulegan–Carpenter numbers

Published online by Cambridge University Press:  26 August 2009

RAHUL A. BIDKAR ,
MARK KIMBER ,
ARVIND RAMAN ,
ANIL K. BAJAJ  and
SURESH V. GARIMELLA
RAHUL A. BIDKAR
Affiliation:
Dynamic Systems and Stability Lab, School of Mechanical Engineering & Birck Nanotechnology Center, 585 Purdue Mall, Purdue University, West Lafayette, Indiana 47907, USA
MARK KIMBER
Affiliation:
Thermal Microsystems Lab, School of Mechanical Engineering & Birck Nanotechnology Center, 585 Purdue Mall, Purdue University, West Lafayette, Indiana 47907, USA
ARVIND RAMAN*
Affiliation:
Dynamic Systems and Stability Lab, School of Mechanical Engineering & Birck Nanotechnology Center, 585 Purdue Mall, Purdue University, West Lafayette, Indiana 47907, USA
ANIL K. BAJAJ
Affiliation:
Dynamic Systems and Stability Lab, School of Mechanical Engineering & Birck Nanotechnology Center, 585 Purdue Mall, Purdue University, West Lafayette, Indiana 47907, USA
SURESH V. GARIMELLA
Affiliation:
Thermal Microsystems Lab, School of Mechanical Engineering & Birck Nanotechnology Center, 585 Purdue Mall, Purdue University, West Lafayette, Indiana 47907, USA
*
†Email address for correspondence: raman@ecn.purdue.edu
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Abstract

Slender sharp-edged flexible beams such as flapping wings of micro air vehicles (MAVs), piezoelectric fans and insect wings typically oscillate at moderate-to-high values of non-dimensional frequency parameter β with amplitudes as large as their widths resulting in Keulegan–Carpenter (KC) numbers of order one. Their oscillations give rise to aerodynamic damping forces which vary nonlinearly with the oscillation amplitude and frequency; in contrast, at infinitesimal KC numbers the fluid damping coefficient is independent of the oscillation amplitude. In this article, we present experimental results to demonstrate the phenomenon of nonlinear aerodynamic damping in slender sharp-edged beams oscillating in surrounding fluid with amplitudes comparable to their widths. Furthermore, we develop a general theory to predict the amplitude and frequency dependence of aerodynamic damping of these beams by coupling the structural motions to an inviscid incompressible fluid. The fluid–structure interaction model developed here accounts for separation of flow and vortex shedding at sharp edges of the beam, and studies vortex-shedding-induced aerodynamic damping in slender sharp-edged beams for different values of the KC number and the frequency parameter β. The predictions of the theoretical model agree well with the experimental results obtained after performing experiments with piezoelectric fans under vacuum and ambient conditions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 269 - 289
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Ansari, S. A., Zbikowski, R. & Knowles, K. 2006 Aerodynamic modelling of insect-like flapping flight for micro air vehicles. Prog. Aerosp. Sci. 42, 129–172.CrossRefGoogle Scholar
Bürmann, P., Raman, A. & Garimella, S. V. 2002 Dynamics and topology optimization of piezoelectric fans. IEEE Trans. Compon. Packag. Technol. 25 (4), 592–600.CrossRefGoogle Scholar
Chu, W. H. 1963 Vibration of fully submerged cantilever plates in water. Tech Rep. 2. Southwest Research Institute, TX.Google Scholar
Clements, R. R. 1973 Inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.CrossRefGoogle Scholar
Ewins, D. J. 2000 Modal Testing: Theory, Practice, and Application, 2nd ed. Baldock.Google Scholar
Fu, Y. & Price, W. G. 1987 Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid. J. Sound Vib. 118 (3), 495–513.CrossRefGoogle Scholar
Graham, J. M. R. 1980 The forces on sharp-edged cylinders in oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 97 (2), 331–346.CrossRefGoogle Scholar
Jones, M. A. 2003 The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496, 405–441.CrossRefGoogle Scholar
Keulegan, G. H. & Carpenter, L. H. 1958 Forces on cylinders and plates in an oscillating fluid. J. Res. Natl Bur. Stand. 60 (5), 423–440.CrossRefGoogle Scholar
Kimber, M., Garimella, S. V. & Raman, A. 2007 Local heat transfer coefficients induced by piezo electrically actuated vibrating cantilevers. J. Heat Trans.-ASME 129, 1168–1176.CrossRefGoogle Scholar
Krasny, R. 1986 Desingulariztion of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292–313.CrossRefGoogle Scholar
Maull, D. J. & Milliner, M. G. 1978 Sinusoidal flow past a circular cylinder. Coast. Engng 2, 149–168.CrossRefGoogle Scholar
Meirovitch, L. 2000 Principles and Techniques of Vibrations, 2nd ed. Prentice Hall.Google Scholar
Meyerhoff, W. K. 1970 Added mass of thin rectangular plates calculated from potential theory. J. Ship Res. 14, 100–111.CrossRefGoogle Scholar
Nayfeh, A. & Mook, D. 1979 Nonlinear Oscillations, 1st ed. John Wiley & Sons.Google Scholar
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139–161.CrossRefGoogle Scholar
Sader, J. E. 1998 Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys. 84, 64–76.CrossRefGoogle Scholar
Sarpkaya, T. 1963 Lift, drag, and added-mass coefficients for a circular cylinder immersed in a time-dependent flow. J. Appl. Mech.-Trans. ASME 30 (1), 13–15.CrossRefGoogle Scholar
Sarpkaya, T. 1975 a Inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined flat plate. J. Fluid Mech. 68, 109–128.CrossRefGoogle Scholar
Sarpkaya, T. 1975 b Forces on cylinders and spheres in a sinusoidally oscillating fluid. J. Appl. Mech.-Trans. ASME 42, 32–37.CrossRefGoogle Scholar
Sarpkaya, T. 1976 Vortex shedding and resistance in harmonic flow about smooth and rough circular cylinders at high Reynolds numbers. Tech Rep. NPS-59SL76021. Naval Postgraduate School, CA.Google Scholar
Sarpkaya, T. 1989 Computational methods with vortices–The 1988 Freeman scholar lecture. J. Fluid Engng-Trans. ASME 111, 5–52.CrossRefGoogle Scholar
Sarpkaya, T. 1995 Hydrodynamic damping, flow-induced oscillations, and biharmonic response. J. Offshore Mech. Arct. 117, 232–238.CrossRefGoogle Scholar
Sarpkaya, T. & Isaacson, M. 1981 Mechanics of Wave Forces on Offshore Structures, 1st ed. Van Nostrand Reinhold.Google Scholar
Stansby, P. K. 1977 Inviscid model of vortex shedding from a circular-cylinder in steady and oscillatory far flows. P. I. Civil Engng Pt. 2 63, 865–880.Google Scholar
Tao, L. & Thiagarajan, K. 2003 a Low KC flow regimes of oscillating sharp edges I. Vortex shedding observation. Appl. Ocean Res. 25, 21–35.CrossRefGoogle Scholar
Tao, L. & Thiagarajan, K. 2003 b Low KC flow regimes of oscillating sharp edges II. Hydrodynamic forces. Appl. Ocean Res. 25, 53–62.CrossRefGoogle Scholar
Taylor, G. 1952 Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. Ser.-A 214, 158–183.Google Scholar
Tuck, E. O. 1969 Calculation of unsteady flows due to small motions of cylinders in a viscous fluid. J. Engng Math. 3 (1), 29–44.CrossRefGoogle Scholar
Wait, S. M., Basak, S., Garimella, S. V. & Raman, A. 2007 Piezoelectric fans using higher flexural modes for electronics cooling applications. IEEE Trans. Compon. Packag. Technol. 30 (1), 119–128.CrossRefGoogle Scholar