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Unsteady Stokes Flow for a Vibrating Cantilever Under a Free-Surface

[+] Author Affiliations
Giovanni Di Ilio, Iskender Sahin, Angelantonio Tafuni

New York University, Brooklyn, NY

Paper No. IMECE2014-36929, pp. V009T12A003; 8 pages
doi:10.1115/IMECE2014-36929
From:
  • ASME 2014 International Mechanical Engineering Congress and Exposition
  • Volume 9: Mechanics of Solids, Structures and Fluids
  • Montreal, Quebec, Canada, November 14–20, 2014
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4958-3
  • Copyright © 2014 by ASME

abstract

Vibration of a thin, rectangular-cross-section beam submerged in a viscous, quiescent fluid undergoing small amplitude oscillations is studied using a Boundary Element (BE) approach in which the free-surface is modeled through a stress-free boundary condition. The Stokes approximation is used where nonlinear convective terms are negligible and the problem is formulated in Fourier and Laplace transform space when appropriate. Results are expressed in terms of non-dimensional hydrodynamic force and its components, namely added mass and damping coefficients. Several parametric studies are conducted to evaluate the effects of depth of submergence, frequency and the amplitude of oscillations on the hydrodynamic functions. The results are compared with the classical solution for a vibrating lamina in an infinite fluid as the limit case and with a recent study using Smoothed Particle Hydrodynamics (SPH) analysis in the presence of a free-surface.

Copyright © 2014 by ASME

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