Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 185351, 19 pages
Research Article

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Demian G. Silva1 and Paulo S. Varoto2

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.