  The phonon propagation dynamics in a phononic crystal waveguide, realized via
a suspended one-dimensional membrane array with periodic air holes, is
investigated as function of its geometry. The bandstructure of the phononic
crystal can be engineered by modifying the characteristics of the phonon
standing waves in the waveguide by varying the waveguide width and the pitch of
the air holes. This enables the phonon transmission bands, the bandgaps, the
velocity and the nonlinear dispersion in the phononic crystal to be controlled.
Indeed the engineered bandstructure can also be tuned to sustain multiple
phonon modes in a given branch which whilst being spectrally degenerate can be
temporally resolved via their differing group velocities. This systematic study
reveals the key geometric parameters that enable the phonon transport in
phononic crystal waveguides to be fully controlled.
