In this article, we compare the performance of a tuned-mass damper mounted at the end of a cantilever beam to the Lanchester damper which was shown in the previous article. The classic single-degree-of-freedom (SDOF) tuned-mass damper is sketched in the figure below. The design approach is to find the equivalent SDOF system for the cantilever beam’s mode of interest and then use the design formulas for an optimal SDOF TMD to determine the stiffness and damping of the absorber.
In this article, we show the robust and broadband performance of a Lanchester damper applied to a cantilever beam and how it achieves good performance without tuning and good performance over a number of modes, not just the primary mode.
Beams are often used in precision engineering applications. One common question is “what are the optimal support locations for a beam?” The answer depends on the desired objective. Below we describe some of the most common support locations: Airy points, Bessel points, minimum deflection, and nodal points. It turns out that these points are relatively close to each other for the uniform beam. The basic problem is sketched in the figure below. A uniform beam is supported on two points and the objective is the determine the placement of the supports in the presence of gravity.