Rahul A. Bidkar

Purdue University, West Lafayette, Indiana, United States

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Publications (6)8.03 Total impact

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    Rahul A. Bidkar, Daniel A. McAdams
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    ABSTRACT: In this article, a mathematical framework to automatically evaluate the manufacturability of injection-molded and die-cast parts is presented. The framework includes an implemented mathematical algorithm to solve key outstanding challenges in feature recognition for manufacturability analysis of injection-molded and die-cast parts. A novel feature recognition method is developed that is based on decomposing the part into elemental cubes and then, making use of their individual manufacturability, the manufacturability of the part as a whole is evaluated. This article discusses a procedure to obtain a 3D binary representation of the solid model and develops feature recognition techniques to extract critical manufacturability information from this 3D binary array. The outstanding challenges addressed by the method presented include the finding of parting surfaces, parting lines, undercuts, holes, bosses, and finding the direction of mold closure in the context of injection-molded or die-cast parts. The algorithm is implemented using a combination of C++code and Unigraphics solid modeling software. A short example is presented.
    Research in Engineering Design 01/2010; 21(1):1-24. · 1.94 Impact Factor
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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 01/2009; · 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 01/2009; · 3.79 Impact Factor
  • Rahul A. Bidkar, Arvind Raman, Anil K. Bajaj
    Journal of Applied Mechanics. 01/2008; 75(4).
  • Rahul A Bidkar
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    ABSTRACT: The research presented in this dissertation focuses on fluid-structure interactions of thin flexible structures for three different problems, namely, the aeroelastic flutter of webs and ribbons, the nonlinear aerodynamic damping of slender beams, and the gas damping of microcantilevers. All these problems involve flexible structures at different length scales resulting in different physical regimes for the surrounding fluid flows, which are modeled using simplified fluid flow models. The first part of this dissertation presents a theoretical investigation of the aeroelastic flutter of tensioned wide webs and narrow ribbons commonly used in the paper-handling, textile, and sheet-metal industries. The web or ribbon is modeled as a uni-axially tensioned Kirchhoff plate with vanishingly small bending stiffness and is submerged in an incompressible inviscid fluid flow across its free edges resulting in a coupled non-conservative dynamical system with gyroscopic and circulatory terms. Wide webs mainly destabilize through a divergence instability due to cross-flow-induced, conservative centrifugal effects, and for certain values of applied tension, destabilize via a weak flutter instability, due to the wake-induced non-conservative effects. Contrarily, narrow ribbons in cross flow exhibit either flutter or divergence instability depending on the value of applied tension. Wind tunnel experiments, conducted to qualitatively corroborate these theoretical results, were inconclusive due to the lack of sufficient control over the important physical parameters. Nonetheless, the experiments show interesting dynamical phenomena such as simultaneous occurrence of oscillatory and zero frequency response of ribbons. The second part of this dissertation focuses on the nonlinear aerodynamic damping of slender, sharp-edged beams commonly found in flapping wings of micro-air-vehicles (MAVs), piezoelectric fans and insect wings. When such structures oscillate at moderate to large non-dimensional frequencies with large amplitudes comparable to their widths, vortex-shedding from the beam's sharp edges gives rise to nonlinear aerodynamic damping. In this work, a general theory is developed to predict the amplitude and frequency dependence of this aerodynamic damping by coupling the structural motions to an inviscid, incompressible fluid. The fluid-structure interaction model developed here accounts for separation of flow and studies vortex-shedding-induced aerodynamic damping in slender, sharp-edged beams for different values of the Keulegan-Carpenter number and the non-dimensional frequency parameter. The theoretical predictions are validated against carefully performed experiments with piezoelectric fans under vacuum and atmospheric conditions. The third part of this dissertation studies the gas damping of microcantilevers oscillating in different vibration modes in an unbounded gas at low ambient pressures varying over 6 orders of magnitude. The accurate prediction of gas damping of microcantilevers at low ambient pressures is essential for improving the sensitivity of microcantilever-based sensors and improving the efficiency of microresonators. In this work, solutions of a sub-continuum, quasisteady Boltzmann equation with a simplified ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator are used to provide a closed-form fit, which can be used to predict the gas damping of different microcantilever vibration modes. The fit is uniformly valid over 5 orders of magnitude of the Knudsen number and spans the free-molecular, the transition, and the lower pressure side of the slip flow regime. For the higher pressure side of the slip flow regime, this work proposes a boundary-integral-method-based approach for including the slip boundary condition in existing continuum regime models. Detailed experimental data on gas damping of silicon microcantilevers obtained from research collaborators shows excellent agreement with the predictions of the ES-BGK-model-based fit.
    ETD Collection for Purdue University. 01/2008;
  • [Show abstract] [Hide abstract]
    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.
    Research Publications.