Journal
JOURNAL OF SOUND AND VIBRATION
Volume 332, Issue 23, Pages 6169-6176Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsv.2013.06.032
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Funding
- Tshwane University of Technology (TUT)
- National Research Foundation (NRF) of South Africa (NRF) [IFR2011041200002]
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Bryan's effect is the phenomenon of the rotation of the vibration pattern within the body of a rotating, vibrating body. In this paper we generalise Rayleigh's dissipation function whereby we include isotropic, nonlinear damping in the Euler-Lagrange equations. We then derive the equations of motion of a slowly rotating, vibrating, symmetric body. In so doing we analyse the effect that such damping has on Bryan's effect. Using a combination of linear and nonlinear damping in the equations of motion of a slowly rotating symmetric body, a numerical experiment indicates that underdamping, critical damping and overdamping scenarios appear to exist. For the underdamped case we compare the effect on amplitude of vibration made by linear, quadratic and a combination of these types of damping. Our final result for light, isotropic, nonlinear damping, mimicks a known result for light, isotropic, linear damping, namely for a slowly rotating symmetric body, Bryan's effect is invariant and the rate of rotation of the damped pattern is the same as it would be for the pattern of an ideal slowly rotating symmetric body. (C) 2013 Elsevier Ltd. All rights reserved.
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