Extended Plane Wave Expansion Formulation for Viscoelastic Phononic Thin Plates

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.