  We study the low frequency wave propagation behavior of sandwich beams
containing periodically embedded internal resonators. A closed form expression
for the propagation constant is obtained using a phased array approach and
verified using finite element simulations. We show that local resonance and
Bragg bandgaps coexist in such a system and that the width of both bandgaps is
a function of resonator parameters as well as their periodicity. The
interaction between the two bandgaps is studied by varying the local resonance
frequency. We find that a single combined bandgap does not exist for this
system and that the Bragg bandgaps transition into sub-wavelength bandgaps when
the local resonance frequency is above their associated classical Bragg
frequency.
