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Research Papers

Vibration Induced Directed Transport of Particles

[+] Author and Article Information
Ch. Viswarupachari

NVH CAE, Tata Motors Limited, Pune, 411 018, Indiaviswam.chandrapati@tatamotors.com

Anirvan DasGupta1

Department of Mechanical Engineering and Center for Theoretical Studies, Indian Institute of Technology, Kharagpur, 721 302, Indiaanir@mech.iitkgp.ernet.in

S. Pratik Khastgir

Department of Physics and Meteorology and Center for Theoretical Studies, Indian Institute of Technology, Kharagpur, 721 302, Indiapratik@phy.iitkgp.ernet.in

1

Corresponding author.

J. Vib. Acoust 134(5), 051005 (Jun 05, 2012) (6 pages) doi:10.1115/1.4006412 History: Received January 29, 2011; Revised February 03, 2012; Published June 04, 2012; Online June 05, 2012

This paper reports a study on directed transport of a particle over a flat horizontal rigid plate vibrating asymmetrically in its plane. A friction model with both dry and viscous friction terms has been considered. Nonlinear frictional interaction between the particle and the plate, and asymmetry in the vibrations of the plate are essential for the transport process. Two kinds of asymmetry, namely spatial asymmetry, and temporal asymmetry in the plate vibrations have been considered. The mechanism of transport and the transport properties for both kinds of input motion have been clearly brought out. Three nondimensional parameters are found to characterize the transport properties. Two energy metrics have been defined to study and understand the efficiency of the transport process.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

(a) Spatially asymmetric (SA) plate motion corresponding to Eq. 7 with A2/A1=0.5, A3/A1=0.125, ω2/ω1=2 and ω3/ω1=3; (b) Temporally asymmetric (TA) plate motion corresponding to Eq. 8 with A2/A1=0.25, A3/A1=0.04, ω2/ω1=2 and ω3/ω1=3

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Figure 3

(a) Nondimensional inertia force on a particle in the case of SA plate motion (dashed line represents the nondimensional static friction force limit α=2.1); (b) Scaled nondimensional dry friction force on a particle static in the inertial frame for the case of TA plate motion

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Figure 4

Variation of particle drift velocity with α for different values of β and r=0.01 under SA plate motion

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Figure 5

Variation of drift velocity with β for certain values of α

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Figure 6

Variation of particle drift velocity with α for different values of β and r=0.01 under TA plate motion

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Figure 10

Variation of energy ratio ⟨E⟩/E with α for different values of β for TA plate motion

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Figure 9

Time history of particle motion for SA plate motion with β=0.75, r=0.05 (a) α=0.8 and (b) α=2.4

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Figure 8

Variation of energy ratio ⟨E⟩/E with α for different values of β for SA plate motion

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Figure 7

Variation of particle drift velocity with α for different values of β and r=0.1 under TA plate motion

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Figure 1

Schematic diagram of a vibratory particle transport system

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