Using the Mass Ratio to Induce Band Gaps in a 1D Array of Nonlinearly Coupled Oscillators

A one dimensional system of nonlinearly coupled magnetic oscillators has been studied. After deriving the equations of motion for each oscillator, the system is linearized about a stable equilibrium and studied using an assumed solution form for a traveling wave. Wave propagation and attenuation regions are predicted by reducing the system of equations to a standard eigenvalue problem. Through evaluating these equations across the entire irreducible Brillouin zone, it is determined that when the masses of each oscillator are identical, the entire frequency range of the system is a propagation zone. By varying the masses comprising a unit cell, band gaps are observed. It is shown that the mass ratio can be used to guide both the size and location of these band gaps. Numerical simulations are performed to support our analytical findings.