The effect of discrete viscous damping on the transverse vibration of beams
The effect of a discrete elastic element on the transverse vibration of a Bernoulli-Euler beam has been well-studied; however, the same cannot be said for a beam with a viscous damper. While the former can be analyzed via separation of variables and the solution of the eigenvalue problem, this article presents a method for computing the resonances of the latter case. The nature of a discrete viscous damper's effect on the fundamental frequency of a beam is revealed as the method is applied to the case of a cantilevered beam. In this process, it is shown that damping has the capacity to increase the fundamental frequency of the beam, and that there exists both a particular location and critical value of damping that maximize this frequency.
Pierson, Harry, Jerald Brevick, and Kevin Hubbard. "The effect of discrete viscous damping on the transverse vibration of beams." Journal of Sound and Vibration 332, no. 18 (2013): 4045-4053.
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