  The resonance modes and the related effects to the transmission of elastic
waves in a two dimensional phononic crystal formed by periodic arrangements of
a two blocks unit cell in one direction are studied. The unit cell consists of
two asymmetric elliptic cylinders coated with silicon rubber and embedded in a
rigid matrix. The modes are obtained by the semi-analytic method in the least
square collocation scheme and confirmed by the finite element method
simulations. Two resonance modes, corresponding to the vibration of the
cylinder along the long and short axes, give rise to resonance reflections of
elastic waves. One mode in between the two modes, related to the opposite
vibration of the two cylinders in the unit cell in the direction along the
layer, results in the total transmission of elastic waves due to zero effective
mass density at the frequency. The resonance frequency of this new mode changes
continuously with the orientation angle of the elliptic resonator.
