Loading...

Closed-form solution of natural frequencies of a cantilever beam under longitudinal rotation of the support

Esmaeili, M ; Sharif University of Technology | 2005

294 Viewed
  1. Type of Document: Article
  2. DOI: 10.1115/detc2005-84830
  3. Publisher: American Society of Mechanical Engineers , 2005
  4. Abstract:
  5. This paper presents the modeling steps towards development of frequency equations for a cantilever beam with a tip mass under general base excitations. More specifically, the beam is considered to vibrate in all the three directions, while subjected to a base rotational motion around its longitudinal direction. This is a common configuration utilized in many vibrating beam gyroscopes and well drilling systems. The governing equations are derived using Extended Hamilton's Principle with general 6-DOF base motion. The natural frequency equations are then extracted in closed-form for the case where the base undergoes longitudinal rotation. For validation purposes, the resulting natural frequencies are compared with two example case studies; one with a beam on a stationary base and the other one with a rotor having flexible shaft. Copyright © 2005 by ASME
  6. Keywords:
  7. Degrees of freedom (mechanics) ; Electric excitation ; Natural frequencies ; Rotation ; Shafts (machine components) ; Base longitudinal rotation ; Cantilever beams with tip mass ; Extended Hamilton's Principle ; Frequency equations ; Cantilever beams
  8. Source: DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, 24 September 2005 through 28 September 2005 ; Volume 1 A , 2005 , Pages 145-151 ; 0791847381 (ISBN); 9780791847381 (ISBN)
  9. URL: https://asmedigitalcollection.asme.org/IDETC-CIE/proceedings-abstract/IDETC-CIE2005/47381/145/316757?redirectedFrom=PDF