Dynamics of a flexible-hub geometrically nonlinear beam with a tip mass

Samir A. Emam

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The dynamics of a flexible-hub geometrically nonlinear beam carrying a tip mass is presented. The hub-beam system is assumed to move in plane and the hub is restrained by a translational and a rotational spring. Hamilton's principle is used to derive the equations of motion and their boundary conditions. A flexural model that takes into account the geometrical coupling between the axial and lateral deformations and ignores the axial deformation and its time derivatives is obtained. An exact solution for the natural frequencies and mode shapes of the free vibration problem is obtained. Using these mode shapes, a reduced-order model of the system is obtained using the Galerkin's method. The dynamic response of the system using the present low-order model shows excellent agreement with the recent finite-element solutions available in the literature.

Original languageEnglish
Pages (from-to)1989-2000
Number of pages12
JournalJVC/Journal of Vibration and Control
Issue number13
Publication statusPublished - Nov 2010


  • Dynamics
  • flexible-hub beam
  • tip mass
  • vibration

ASJC Scopus subject areas

  • Automotive Engineering
  • General Materials Science
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering


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