Comparative analysis of NES and TMD performance via high-dimensional invariant manifolds

A comparative study between a tuned mass damper (TMD) and a nonlinear energy sink (NES), attached to a linear two-degree-of-freedom (DoF) mechanical system under impulsive excitation, is performed. The analysis involves different scenarios; namely, we consider the cases in which only one or both modes of the primary system are initially excited. First, exploiting a harmonic balance approach, the invariant manifolds describing the slow dynamics of the system are identified. Then, introducing the so-called relative dissipation power, the performance of the two absorbers is carefully compared, based on analytical computations. Results illustrate that the two absorbers have similar performance, albeit resorting to different mechanical properties: The NES achieve a broad frequency band of operation exploiting nonlinearity, while the TMD by increasing damping. An interesting feature, highlighted by the invariant manifold, is that the NES is generally unable to resonate with more than one mode of the primary system at the same time, rather, it experiences a sort of modal cascade.