Rahul A. Bidkar

Purdue University, West Lafayette, Indiana, United States

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Publications (5)7.2 Total impact

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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 beta with amplitude as large as their widths resulting in Keulegan-Carpenter (KC) numbers or 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 beta. The predictions of the theoretical model agree well with the experimental results obtained after performing experiments with piezoelectric fans under vacuum and ambient conditions.
    Journal of Fluid Mechanics 09/2009; DOI:10.1017/S0022112009007228 · 2.29 Impact Factor
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    ABSTRACT: Predicting the gas damping of microcantilevers oscillating in different vibration modes in unbounded gas at low pressures is relevant for increasing the sensitivity of microcantilever-based sensors. While existing free-molecular theories are valid only at very high Knudsen numbers, continuum models are valid only at very low Knudsen numbers. We solve the quasisteady Boltzmann equation and compute a closed-form fit for gas damping of rectangular microcantilevers that is valid over four orders of magnitude of Knudsen numbers spanning the free-molecular, the transition, and the low pressure slip flow regimes. Experiments are performed using silicon microcantilevers under controlled pressures to validate the theory.
    Applied Physics Letters 04/2009; 94(16). DOI:10.1063/1.3122933 · 3.52 Impact Factor
  • Rahul A. Bidkar, Arvind Raman, Anil K. Bajaj
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    ABSTRACT: Uni-axially tensioned wide webs and narrow ribbons commonly used in the paper-handling, textile, sheet-metal, and plastics industries are known to undergo large amplitude vibrations characterized as aeroelastic flutter. The aeroelastic stability of stationary wide webs and narrow ribbons coupled with fluid flow across the free edges of the web or ribbon is investigated in this article. The web or ribbon is modeled as a uni-axially tensioned Kirchhoff plate with vanishingly small bending stiffness. The 3D unsteady fluid flow surrounding the web or ribbon is evaluated numerically by using the vortex-lattice method. Wide webs are mainly found to exhibit the divergence instability. For some values of the applied tension, the clustered web modes exhibit frequency curve veering accompanied by a weak flutter instability before the occurrence of the divergence instability. The applied tension plays a critical role in deciding the type of instability in narrow ribbons. In cross flow, depending on the applied tension, narrow ribbons undergo flutter instability or divergence instability or the simultaneous onset of both instabilities.
    Journal of Applied Mechanics 07/2008; 75(4). DOI:10.1115/1.2871192 · 1.40 Impact Factor
  • Rahul A. Bidkar, Arvind Raman, Anil K. Bajaj
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    ABSTRACT: Aero elastic flutter may play an important role in the breakage of thin membrane-like structures (a.k.a. webs) found in paper-handling, textile, sheet-metal and magnetic tapes industry. In this article, we examine the aero elastic stability of a web modeled as a uni-axially tensioned (along the machine direction) low aspect ratio Kirchhoff plate, which is subject to a fluid flow in the cross machine direction. Panel methods based on the distribution of singularity solutions (sources and doublets) on the surface of the web are used to numerically solve the problem of 3D unsteady potential flow surrounding the web. The equation of motion of the plate coupled to a fluid flow is discretized by using Galerkin’s method. The discretization is performed in the configuration space formulation of the gyroscopic eigenvalue problem. The linear stability of this reduced order system is investigated. The onset of flutter instability as a function of base fluid flow in the cross machine direction is studied. The effects of fluid coupling on the frequencies and modes of oscillations of the web are also studied.
    ASME 2005 International Mechanical Engineering Congress and Exposition; 01/2005
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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.