  We investigate the dispersion characteristics of locally resonant elastic
metamaterials formed by the erection of pillars on the solid regions in a plate
patterned by a periodic array of holes. We show that these solid regions
effectively act as springboards leading to an enhanced resonance behavior by
the pillars when compared to the nominal case of pillars with no holes. This
local resonance amplification phenomenon, which we define as the "trampoline
effect", is shown to cause subwavelength band gaps to increase in size by up to
a factor of 4. This outcome facilitates the utilization of subwavelength
metamaterial properties over exceedingly broad frequency ranges.
