0
Research Papers

Exact Frequency Analysis of a Rotating Cantilever Beam With Tip Mass Subjected to Torsional-Bending Vibrations

[+] Author and Article Information
Masoud Ansari1

Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canadam3ansari@uwaterloo.ca

Ebrahim Esmailzadeh2

Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canadaezadeh@uoit.ca

Nader Jalili

Department of Mechanical and Industrial Engineering, Piezoactive Systems Laboratory, Northeastern University, Boston, MA 02115n.jalili@neu.edu

P(κ)=A1(sin(λκ)sinh(λκ))+A2(cos(λκ)cosh(λκ)) (Eq. (41) of Ref. 26).

Q(κ)=B1sin(λ2γκ) (Eq. (42) of Ref. 26).

PIV+(IxbL2Ω32/EI)P(λ4)P+(IxbΩ3iLλ21/ρbEI)Q=0 (Eq. (48) of Ref. 26).

Q+(Ixbλ4γ2/ρbL4)Q(IxbΩ3iλ2λ1/GJρbL4)P=0 (Eq. (49) of Ref. 26).

1

Present address: Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada.

2

Corresponding author.

J. Vib. Acoust 133(4), 041003 (Apr 06, 2011) (9 pages) doi:10.1115/1.4003398 History: Received August 05, 2009; Revised November 01, 2010; Published April 06, 2011; Online April 06, 2011

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Beam having torsional and bending vibrations subjected to base rotation

Grahic Jump Location
Figure 2

Kinematics of the end mass attached to a rotating slender beam

Grahic Jump Location
Figure 3

Variations in the real part of the natural frequencies with the base rotation

Grahic Jump Location
Figure 4

Variations in the imaginary part of the natural frequencies with the base rotation

Grahic Jump Location
Figure 5

Variations in the real part of the natural frequencies with end mass (Ω=20 rad/s)

Grahic Jump Location
Figure 6

Variations in the imaginary part of natural frequencies with end mass (Ω=20 rad/s)

Grahic Jump Location
Figure 7

Variations in the real part of natural frequencies with the mass length (Ω=20 rad/s)

Grahic Jump Location
Figure 8

Variations in the imaginary part of natural frequencies with the mass length (Ω=20 rad/s)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In