An exact frequency analysis of a rotating beam with an attached tip mass is addressed in this paper while the beam undergoes coupled torsional-bending vibrations. The governing coupled equations of motion and the corresponding boundary condition are derived in detail using the extended Hamilton principle. It has been shown that the source of coupling in the equations of motion is the rotation and that the equations are linked through the angular velocity of the base. Since the beam-tip-mass system at hand serves as the building block of many vibrating gyroscopic systems, which require high precision, a closed-form frequency equation of the system should be derived to determine its natural frequencies. The frequency analysis is the basis of the time domain analysis, and hence, the exact frequency derivation would lead to accurate time domain results, too. Control strategies of the aforementioned gyroscopic systems are mostly based on their resonant condition, and hence, acquiring knowledge about their exact natural frequencies could lead to a better control of the system. The parameter sensitivity analysis has been carried out to determine the effects of various system parameters on the natural frequencies. It has been shown that even the undamped systems undergoing base rotation will have complex eigenvalues, which demonstrate a damping-type behavior.
Skip Nav Destination
e-mail: m3ansari@uwaterloo.ca
e-mail: ezadeh@uoit.ca
e-mail: n.jalili@neu.edu
Article navigation
August 2011
Research Papers
Exact Frequency Analysis of a Rotating Cantilever Beam With Tip Mass Subjected to Torsional-Bending Vibrations
Masoud Ansari,
Masoud Ansari
Faculty of Engineering and Applied Science,
e-mail: m3ansari@uwaterloo.ca
University of Ontario Institute of Technology
, 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canada
Search for other works by this author on:
Ebrahim Esmailzadeh,
Ebrahim Esmailzadeh
Professor
Fellow ASME
Faculty of Engineering and Applied Science,
e-mail: ezadeh@uoit.ca
University of Ontario Institute of Technology
, 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canada
Search for other works by this author on:
Nader Jalili
Nader Jalili
Department of Mechanical and Industrial Engineering, Piezoactive Systems Laboratory,
e-mail: n.jalili@neu.edu
Northeastern University
, Boston, MA 02115
Search for other works by this author on:
Masoud Ansari
Faculty of Engineering and Applied Science,
University of Ontario Institute of Technology
, 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canadae-mail: m3ansari@uwaterloo.ca
Ebrahim Esmailzadeh
Professor
Fellow ASME
Faculty of Engineering and Applied Science,
University of Ontario Institute of Technology
, 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canadae-mail: ezadeh@uoit.ca
Nader Jalili
Department of Mechanical and Industrial Engineering, Piezoactive Systems Laboratory,
Northeastern University
, Boston, MA 02115e-mail: n.jalili@neu.edu
J. Vib. Acoust. Aug 2011, 133(4): 041003 (9 pages)
Published Online: April 6, 2011
Article history
Received:
August 5, 2009
Revised:
November 1, 2010
Online:
April 6, 2011
Published:
April 6, 2011
Citation
Ansari, M., Esmailzadeh, E., and Jalili, N. (April 6, 2011). "Exact Frequency Analysis of a Rotating Cantilever Beam With Tip Mass Subjected to Torsional-Bending Vibrations." ASME. J. Vib. Acoust. August 2011; 133(4): 041003. https://doi.org/10.1115/1.4003398
Download citation file:
Get Email Alerts
Related Articles
Experimental Studies on Active Vibration Control of a Beam Using Hybrid Active∕Passive Constrained Layer Damping Treatments
J. Vib. Acoust (October,2005)
Combined Torsional-Bending-Axial Dynamics of a Twisted Rotating Cantilever Timoshenko Beam With Contact-Impact Loads at the Free End
J. Appl. Mech (May,2007)
Lagrangian Formulation of Rotating Beam With Active Constrained Layer Damping in Time Domain Analysis
J. Mech. Des (March,2004)
Modeling and Analysis of a Piezoelectric Energy Scavenger for Rotary Motion Applications
J. Vib. Acoust (February,2011)
Related Proceedings Papers
Related Chapters
Mechanics of Long Beam Columns
Mechanics of Drillstrings and Marine Risers
Fundamentals of Structural Dynamics
Flow Induced Vibration of Power and Process Plant Components: A Practical Workbook
Engineering Design about Electro-Hydraulic Intelligent Control System of Multi Axle Vehicle Suspension
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)