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Parameter Sensitivity Analysis of Rotating Beams in Frequency Domain

[+] Author Affiliations
Masoud Ansari

University of Waterloo, Waterloo, ON, Canada

Ebrahim Esmailzadeh

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

Nader Jalili

Clemson University, Clemson, SC

Paper No. DETC2009-87686, pp. 1479-1484; 6 pages
doi:10.1115/DETC2009-87686
From:
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4898-2 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME

abstract

Many mechanical rotating systems can be modeled as a cantilever beam attached to a rotating substrate. Vibratory beam gyroscopes are good examples of such systems. They consist of a rotating beam with a tip mass, attached to a rotating base. Due to the base rotation, the governing partial differential equations of the system are coupled, and hence, the system undergoes coupled torsional-bending vibrations. The coupling effect complicates the frequency analysis of the system, especially in determining the system characteristic equation. Many investigators have chosen to use the assumed mode method in their analysis of such systems instead of extracting the exact mode shapes of the system. In spite of all these difficulties, this paper addresses the exact frequency analysis of such systems and presents a closed-form frequency characteristic equation and evaluates the accurate values of the natural frequencies. The application of the proposed method is not limited to the system at hand, as it can be utilized for analyzing general systems with coupled governing equations of motion. Having analyzed a closed-form frequency equation has two valuable advantages: a) it can serve as the basis for the subsequent time-domain analysis; and b) it can be very essential in developing control strategies. In this study a thorough sensitivity analysis is performed to determine the effects of different parameters on the natural frequencies of the coupled vibrating system. The proposed method reveals some interesting findings in the systems which were difficult, if not impossible, to be revealed by the assumed mode method commonly utilized in many research work reported recently in literature.

Copyright © 2009 by ASME

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