Complete Band Gaps in Nano-Piezoelectric Phononic Crystals

Abstract

We study the band structure of elastic waves propagating in a nano-piezoelectric phononic crystal consisting of a polymeric matrix reinforced by BaTiO 3 inclusions in square, rectangular, triangular, honeycomb and Kagomé lattices. We also investigate the influence of inclusion cross section geometrycircular, 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.

A Phononic Crystal with Differently Configured Double Defects for Broadband Elastic Wave Energy Localization and Harvesting

“…Band-structure analysis in waves, which is analogous to modal analysis in vibrations, plays a significant role in (1) specifying dispersion relations (eigenfrequencies in an eigenvalue problem) of the PnC and (2) visualizing mode shapes (eigenvectors in an eigenvalue problem) of the PnC at given frequencies [47,48]. Figure 2 depicts the dispersion results of the PnC shown in Figure 1 [49,50]. The x-axis stands for the Bloch wavevectors that belong to the first Brillouin zone (Γ→X→M→Γ) and the y-axis stands for the eigenfrequency, ranging from 70 kHz to 90 kHz.…”

Modelling Propagating Bloch Waves in Magnetoelectroelastic Phononic Structures with Kagomé Lattice Using the Improved Plane Wave Expansion

“…The reciprocal lattice vector is given by , . The structure function is defined as [8]: It should be noted that there are three variations of hexagonal lattice [22], that is to say, triangular, honeycomb (or graphite), and Kagomé lattices. The points of the FIBZ in Figure 1b for Kagomé lattice are Г (0,0), X 2π 3a , 0 and…”

“…The PnCs have many applications, for instance, wave manipulation [3], vibration isolation [4], acoustic filters [5], and waveguides [6]. Furthermore, smart periodic structures have been investigated, for instance, piezoelectric [7,8] and piezomagnetic [9] PnCs. Nevertheless, there are few studies regarding magnetoelectroelastic phononic crystals (MPnCs) [10][11][12][13][14][15].…”

Electro-Mechanical Coupling Properties of Band Gaps in an Elastic/Piezoelectric Phononic Crystal Nonlocal Nanobeam With Periodically Attached “spring-Mass” Resonators

“…Based on transfer matrix (TM) method and nonlocal theory, Chen, Yan and Wang et al studied the anti-plane transverse wave mode [3] , symmetric wave mode [4] and plane wave mode [5] of one-dimensional (1D) layered piezoelectric PC nanostructures in detail. Miranda Jr and Dos Santos [6] calculate the band structures of two-dimensional (2D) piezoelectric PC nanostructures consisting of difform inclusions in kinds of lattices, and research the corresponding properties of band gaps. Based on PWE method, the electro-mechanical coupling bandgap properties of piezoelectric PC nanobeams from the perspectives of surface effects [7] , nonlocal effects [8] and nonlinearity [9] were investigated by Qian et al.…”