  Local resonance band gaps in acoustic metamaterials are widely known for
their strong attenuation yet narrow frequency span. The latter limits the
practical ability to implement subwavelength band gaps for broadband
attenuation and has motivated novel metamaterial designs in recent years. In
this paper, we investigate the behavior of acoustic metamaterials where unit
cells house multiple resonating elements stacked in different configurations,
aimed at instigating a wide array of wave propagation profiles that are
otherwise unattainable. The dispersion mechanics of the multi-resonator
metamaterials are developed using purely analytical expressions which depict
and explain the underlying dynamics of such systems both at the unit cell level
as well as the frequency response of their finite realizations. The framework
reveals the mechanism behind the transition of the lower and upper band gap
bounds in metamaterials with parallel resonators resulting in a significant
band gap widening. The analysis also illustrates the ability of metamaterials
with dual-periodic super cells to exhibit a range of dispersion transitions
culminating in collapsing solutions of acoustic and optic bands, enabling a
coalescence of local resonance band gaps, vanishing resonances, and a number of
intriguing scenarios in between.
