Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 185351, 19 pages
Effects of Variations in Nonlinear Damping Coefficients on the Parametric
Vibration of a Cantilever Beam with a Lumped Mass
1Defense Projects, Empresa Brasileira de Aeronautica (EMBRAER), Avenue Brigadeiro Faria Lima 2170, 12227-901 São José dos Campos, SP, Brazil
2Mechanical Engineering Department, School of Engineering of Sao Carlos, University of Sao Paulo, Avenue Trabalhador Saocarlense 400, 13566-590 São Carlos, SP, Brazil
Received 26 March 2008; Accepted 27 June 2008
Academic Editor: Jose Balthazar
Copyright © 2008 Demian G. Silva and Paulo S. Varoto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Uncertainties in damping estimates can significantly affect the dynamic response
of a given flexible structure. A common practice in linear structural
dynamics is to consider a linear viscous damping model as the major energy
dissipation mechanism. However, it is well known that different forms of
energy dissipation can affect the structure's dynamic response. The major
goal of this paper is to address the effects of the turbulent frictional damping
force, also known as drag force on the dynamic behavior of a typical flexible
structure composed of a slender cantilever beam carrying a lumped-mass
on the tip. First, the system's analytical equation is obtained and solved by
employing a perturbation technique. The solution process considers variations
of the drag force coefficient and its effects on the system's response.
Then, experimental results are presented to demonstrate the effects of the
nonlinear quadratic damping due to the turbulent frictional force on the system's
dynamic response. In particular, the effects of the quadratic damping
on the frequency-response and amplitude-response curves are investigated.
Numerically simulated as well as experimental results indicate that variations
on the drag force coefficient significantly alter the dynamics of the
structure under investigation.