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Analytical Solutions for Nonlinear Lateral Sloshing in Partially-Filled Elliptical Tankers

[+] Author Affiliations
Davood Younesian, Hassan Askari, Zia Saadatnia

Iran University of Science and Technology, Tehran, Iran

Ebrahim Esmailzadeh

University of Ontario Institute of Technology, Oshawa, ON, Canada

Paper No. DETC2011-48468, pp. 135-139; 5 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5478-5
  • Copyright © 2011 by ASME


Dynamic behavior of the large amplitude lateral sloshing is analytically studied in partially filled elliptical tankers. Theory of elliptical trammel pendulums is employed for modeling of the large oscillation of the fluid inside the elliptical container. Nonlinear governing equation of the motion is derived employing the Hamilton principle. Standard and modified Energy Balance Method (EBM) is adopted as the solution technique. Natural frequencies of the free oscillation are analytically obtained as a function of the initial amplitude. It is proved that the nonlinear dynamical system can behave mutually as a hardening and softening system based on the tanker aspect ratio. A number of numerical simulations are carried out and accuracy of the obtained analytical solution is evaluated.

Copyright © 2011 by ASME
Topics: Sloshing , Tankers



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