  The extended plane wave expansion (EPWE) formulation is derived to obtain the
complex band structure of flexural waves in viscoelastic thin phononic crystal
plates considering the Kirchhoff-Love plate theory. The presented formulation
yields the evanescent behavior of flexural waves in periodic thin plates
considering viscoelastic effects. The viscosity is modeled by the standard
linear solid model (SLSM), typically used to closely model the behavior of
polymers. It is observed that the viscoelasticity influences significantly both
the propagating and evanescent Bloch modes. The highest wave attenuation of the
viscoelastic phononic thin plate is found around a unit cell filling fraction
of 0.37 for higher frequencies considering the least attenuated wave mode. This
EPWE formulation broadens the suitable methods to handle evanescent flexural
waves in 2-D thin periodic plate systems considering the effects of
viscoelasticity on wave attenuation.
