Journal of Fluid Mechanics

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

RAHUL A. BIDKARa1, MARK KIMBERa2, ARVIND RAMANa1 c1, ANIL K. BAJAJa1 and SURESH V. GARIMELLAa2

a1 Dynamic Systems and Stability Lab, School of Mechanical Engineering & Birck Nanotechnology Center, 585 Purdue Mall, Purdue University, West Lafayette, Indiana 47907, USA

a2 Thermal Microsystems Lab, School of Mechanical Engineering & Birck Nanotechnology Center, 585 Purdue Mall, Purdue University, West Lafayette, Indiana 47907, USA

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.

(Received June 02 2008)

(Revised March 22 2009)

Correspondence:

c1 Email address for correspondence: raman@ecn.purdue.edu

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