Meta-mass systems: A harbinger for a vibration energy harvesting technology

Abstract

For a limited class of fuzzy structures, the “master” structure is a grounded Newtonian mass wherein are distributed the “fuzzies,” modeled as nearly equal magnitude sprung masses with resonances densely filling a frequency band. We term said system a grounded “meta-mass,” showing a properly designed “meta-mass vibration energy harvester” addresses a fundamental technical obstacle to the harvesting of waste mechanical energy, the so-called “aperture” problem; thereby making meta-mass systems a harbinger for a vibration energy harvesting technology. Shown is the oscillators’ resonances provide ``bounds’’ on the system resonances, the relative “locations” of the system resonances within its bound-pair being determinative of system behavior. Then shown is the value of a certain combination of non-dimensional system measures—twice the fractional bandwidth squared divided by the product of the mass ratio and the natural log of N—is determinative of said relative locations. Finally shown is virtually all the energy inputted impulsively to the Newtonian mass is transferred to the encapsulated oscillators in a time of the order of the inverse of the band of oscillators, for a narrow system subclass wherefore each system resonance is near the center of its bound-pair.