Abstract
We study the band structure of elastic waves propagating in a nano-piezoelectric phononic crystal consisting of a polymeric matrix reinforced by BaTiO3 inclusions in square, rectangular, triangular, honeycomb and Kagome lattices. We also investigate the influence of inclusion cross section geometry - circular, hollow circular, square and rotated square with a 45o angle of rotation with respect to x and y axes. Plane wave expansion method is used to solve the governing equations of motion of a piezoelectric solid based on classical elasticity theory, ignoring nanoscopic size effects, considering two-dimensional periodicity and wave propagation in the xy plane. Complete band gaps between XY and Z modes are observed for all inclusions and the best performance is for circular inclusion in a triangular lattice. Piezoelectricity influences significantly the band gaps for hollow circular inclusion in lower frequencies. We suggest that nano-piezoelectric phononic crystals are feasible for elastic vibration management in GHz.
Highlights
Phononic crystals (PCs) are artificial periodic composites designed to exhibit phononic band gaps and they have been quite studied[1,2,3,4,5,6,7,8,9,10,11,12,13,14]
On the relation between parameters Rand rfor hollow circular inclusion is r = 0.2Rand we do not investigate the influence of BaTiO3 thickness, i.e.R - r,̃ in the band structure
Broad complete band gaps are obtained for a nanopiezoelectric PC, consisting of BaTiO3 inclusions embedded in a polymeric matrix, for different inclusion geometries and different lattices
Summary
Phononic crystals (PCs) are artificial periodic composites designed to exhibit phononic band gaps and they have been quite studied[1,2,3,4,5,6,7,8,9,10,11,12,13,14]. There are no mechanical (elastic or acoustic) propagating waves in phononic band gaps, only evanescent waves. These band gaps are created by the periodically mismatch between the constituent materials. The ability of creating phononic band gaps is similar to the electronic and photonic band gaps in semiconductors and photonic crystals[15,16], respectively. The physical origin of phononic and photonic band gaps can be understood at micro-scale using the classical wave theory to describe the Bragg and Mie resonances, respectively, based on the scattering of mechanical and electromagnetic waves propagating within the crystal[17]
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