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Closed-form solution of natural frequencies of a cantilever beam under longitudinal rotation of the support
, Article 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) ; Durali, M ; Jalili, N ; Sharif University of Technology
American Society of Mechanical Engineers
2005
Abstract
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...