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Research Papers

The Flexural Instability of Spinning Flexible Cylinder Partially Filled With Viscous Liquid

[+] Author and Article Information
R. D. Firouz-Abadi

Department of Aerospace Engineering, Sharif University of Technology, Tehran 11155-8639, Iranfirouzabadi@sharif.edu

H. Haddadpour

Department of Aerospace Engineering, Sharif University of Technology, Tehran 11155-8639, Iranhaddadpour@sharif.edu

J. Appl. Mech 77(1), 011001 (Sep 23, 2009) (9 pages) doi:10.1115/1.3172143 History: Received August 30, 2008; Revised June 06, 2009; Published September 23, 2009

This paper deals with the flexural instability of flexible spinning cylinders partially filled with viscous fluid. Using the linearized Navier–Stokes equations for the incompressible flow, a two-dimensional model is developed for fluid motion. The resultant force exerted on the flexible cylinder wall as the result of the fluid motion is calculated as a function of lateral acceleration of the cylinder axis in the Laplace domain. Applying the Hamilton principle, the governing equations of flexural motion of the rotary flexible cylinder mounted on general viscoelastic supports are derived. Then combining the equations describing the fluid force on the flexible cylinder with the structural dynamics equations, the coupled-field governing equations of the system are obtained. A numerical technique is devised with the obtained model for stability analysis of the flexible cylinder and some examples are presented. The effect of material viscoelasticity and structural damping on the stability margins of the flexible cylinder is examined, and some parameter studies on the governing parameters of the critical spinning speed are carried out.

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Figures

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Figure 1

Schematic of a spinning flexible cylinder partially with liquid

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Figure 6

Critical spinning speed of the cylinder on purely elastic supports for μ=3.0 and various κ

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Figure 5

Critical spinning speed of the cylinder on purely elastic supports for κ=0.6 and various μ

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Figure 4

The effect of material viscoelasticity on the stability margin of the cylinder partially filled with viscous fluid, cases 1 and 2

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Figure 3

The effect of structural damping on the stability margin of the cylinder partially filled with viscous fluid, cases 1 and 2

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Figure 2

Instability analysis graphs for cases 1 and 2: (a) plots of imaginary parts of h and λn versus their real parts, (b) plot of dimensionless spinning frequency Ω/ω∗ against the real part of λn, and (c) plot of dimensionless frequency of the fluid-structure system ω/Ω against the real part of h

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