A revisit of spinning disk models. Part I: Derivation of equations of motion

N. Baddour, J. W. Zu

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Abstract

Previous models of spinning disks have focused on modelling the disk as a spinning membrane. The effect of bending stiffness was then incorporated by adding the appropriate term to the previously derived spinning membrane equation. A pure spinning plate model does not exist in the literature. Furthermore, in both existing linear and nonlinear models of spinning disks, the in-plane inertia and rotary inertia of the disk have been ignored. This paper revisits the derivation of the equations of motion of a spinning plate. The derivation focuses on the use of Hamilton's principle with linear Kirchhoff and nonlinear von Karman strain expressions. In-plane and rotary inertias of the plate are automatically taken into account. The use of Hamilton's principle guarantees the correct derivation of the corresponding boundary conditions. The resulting equations and boundary conditions are discussed.

Original languageEnglish
Pages (from-to)541-559
Number of pages19
JournalApplied Mathematical Modelling
Volume25
Issue number7
DOIs
StatePublished - Jul 2001

Keywords

  • Derivation of equations
  • Hamiltonian
  • Modelling
  • Spinning disk

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