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Non-Linear Free Vibrations of a Rotating Beam Carrying a Tip Mass With Rotary Inertia

[+] Author Affiliations
Ahmad A. Al-Qaisia

University of Jordan, Amman, Jordan

Paper No. PVP2002-1510, pp. 1-8; 8 pages
doi:10.1115/PVP2002-1510
From:
  • ASME 2002 Pressure Vessels and Piping Conference
  • Piping and Component Analysis and Diagnosis
  • Vancouver, BC, Canada, August 5–9, 2002
  • Conference Sponsors: Pressure Vessels and Piping Division
  • ISBN: 0-7918-4658-X
  • Copyright © 2002 by ASME

abstract

The non-linear, for each of the first three modes, of planar, large amplitude flexural free vibrations of a beam clamped with an angle to a rigid rotating hub and carrying a tip mass with rotary inertia are investigated. The shear deformation and rotary inertia effects are assumed to be negligible, but account is taken of axial inertia, non-linear curvature and the inextensibility condition. The Lagrangian dynamics in conjunction with the assumed mode method, assuming constant hub rotation speed, is utilized in deriving the non-linear unimodal temporal problem. The time transformation method is employed to obtain an approximate solution to the frequency-amplitude relation of the beam-mass free vibration, since the order of the nonlinear terms is not small which includes static and inertial geometric stiffening as well as inertial softening terms. Results in non-dimensional form are presented graphically, for the effect beam root-attachment angle, hub radius and the attached inertia element ratio on the variation of the natural frequency with vibration amplitude.

Copyright © 2002 by ASME

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