Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 1: Equations of motion and numerical results

M. Amabili, F. Pellicano, A. F. Vakakis

Research output: Contribution to journalArticlepeer-review

Abstract

The response-frequency relationship in the vicinity of a resonant frequency, the occurrence of travelling wave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell’s nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of four ordinary differential equations by means of the Galerkin method. The radial deflection of the shell is expanded by using a basis of four linear modes. The effect of internal fluid is also investigated. The equations of motion are studied by using a code based on the Collocation Method. The present model is validated by comparison of some results with others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated for the first time; it shows intricate and interesting dynamics.

Original languageEnglish (US)
Pages (from-to)346-354
Number of pages9
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume122
Issue number4
DOIs
StatePublished - Oct 2000

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

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