The effects of small deviations from periodicity on the vibration behavior of coupled arrays of mechanical resonators are investigated, and the consequences for energy propagation across such arrays are described. Existing localization theory is applied to demonstrate that one-dimensional arrays designed as bandpass filters are particularly sensitive to aperiodicity when narrow passband requirements dictate weak inter-resonator coupling. A novel two-dimensional array of resonators is proposed that is less sensitive to disorder than one-dimensional arrays, improving filter performance without the need for improved manufacturing tolerances. Numerical simulations of a simple model are employed to demonstrate the effects of disorder on one- and two-dimensional arrays, and a case study design is discussed that includes statistical investigation using finite-element analysis and experimental measurements of a prototype two-dimensional array.
Weak and strong vibration localization in disordered structures: A statistical investigation