An effective theory for meta-mass and meta-material mechanical/electrical devices

Abstract

A dynamical system comprised of a rigid housing element that encapsulates a large multiplicity of oscillators is said to comprise a “meta-mass,” in that there is no direct interaction of the external environment and the oscillators, the presence of which is inferred in an observed non-Newtonian housing element behavior. For a class of meta-masses, for which the oscillators have more-or-less equal masses with resonances that densely fill a frequency band more-or-less uniformly, the non-Newtonian behavior is most transparently seen in a different “energetics,” i.e., the transfer of energy between the housing element and an external source, this occasioned by an inherently “transitory “internal energy transfer process. Encapsulating a large multiplicity of meta-masses in an ordinary material specimen is said to comprise a meta-material specimen, a somewhat different understanding in not having the direct interaction of each individual oscillator with every other individual oscillator obtain through the behavior of the material matrix. Constructed is a mathematical framework for quantifying limited observable system behavior while not accommodating all underlying physics, i.e., an “effective theory,” this a prerequisite for the design of meta-mass and meta-material mechanical/electrical devices.