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.