Design of mechanical band-pass filters for energy scavenging: Multi-degree-of-freedom models

In this article, a model of a mechanical band-pass filter to be used in energy scavengers is studied. The filter is an ensemble of cantilever beams where at the tip of each beam a mass, known as the proof mass, is mounted. A beam with a proof mass at its tip is called a beam-mass system. The dynamics of a beam-mass system can be represented by its corresponding generalized single-degree-of-freedom (SDoF) system. Using this model, dimensions of the beams and masses of the proof masses of beam-mass systems can be determined, so that an ensemble of such systems would function as a band-pass filter. To verify the adequacy of the SDoF model in representing the dynamics of the infinite-dimensional beam-mass system, a two-degree-of-freedom (TDoF) model of this system is developed. This model affirms that, as far as the energy scavenging is concerned, the SDoF model adequately represents the dynamics of the infinite-dimensional beam-mass system. Consequently, in designing mechanical band-pass filters, it is sufficient to use the SDoF models of the beam-mass systems.