Band Gap Properties of Piezoelectric/Viscous Liquid Phononic Crystals

The viscous effects on the band gap characteristics of the piezoelectric/viscous liquid phononic crystals are studied. The expressions of the generalized eigenvalue equation for the cylindrical phononic crystals are derived. Numerical calculations are performed to discuss the band gap characteristics with different filling ratios and viscous damping parameters. Form the results, it can be observed that the out-of-plane mode will appear, which caused by the viscous effects. Both of the real and imaginary parts of frequencies will increase with the filling fraction becoming larger. The maximum of the normalized band gap width is achieved by f = 0.5. Furthermore, the band gap edges become higher with the viscous damping parameter increasing, especially for higher band gaps.