  We investigate the effect of small spatiotemporal modulations in
subwavelength-dimensioned phononic crystals with large band gaps, on the
frequency spectrum for elastic waves polarized in the plane of periodicity.
When the radius of cylinders periodically placed inside a matrix of
highly-contrasting elastic properties is time-varying, we find that due to the
appearance of frequency harmonics throughout the spectrum, the notion of a band
gap is destroyed in general, although with the appropriate tuning of
parameters, in particular the modulation frequency, it is possible that some
band-gap region is retained, making such systems possible candidates for
tunable bandpass filters or phononic isolators, accordingly, and for sensor
applications.
