Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

Abstract

A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

Theoretical Investigation of Magneto-Electro-Elastic Piezoelectric Phononic Crystal

“…In the frequency region (ω Ob1 , ω Oa1 ), transmission coefficient t = 0 because the absolute values of the elastic coefficients of positive and negative domains are approximately equal. According to our simulation results, the two MPBGs cannot be generated in other piezoelectric phononic crystals [6][7][8][9][10]. If the SRRs are not placed on the opposite sides of the MPPC along the x-axis, the MPBGs will not also be created near the resonance frequencies.…”

“…As a result, the phononic crystal containing a piezoelectric material known as piezoelectric phononic crystals comes to be realized and is studied widely. Vibration energy can be easily converted into electric energy by introducing piezoelectric material within the phononic crystal [6][7][8][9][10].…”

Elastic wave harvesting in piezoelectric-defect-introduced phononic crystal microplates

“…By applying the Bloch periodic boundary conditions [60], the relevant bandgap of the PnCs can be obtained through Eq. (10).…”

“…The phononic crystal (PnC) defect results in a high degree of elastic wave localization and provides an efficient way of energy collection in piezoelectric energy harvesting (PEH) devices, which has attracted much attention [1][2][3][4][5][6]. Bandgap is an extraordinary property of PnCs, and elastic waves in the bandgap frequency range decay rapidly and cannot propagate through the PnCs [7][8][9][10][11]. Furthermore, by changing a single unit cell structure to destroy the periodicity of the PnCs (i.e., a defect), flat passbands (i.e., defect bands) usually appear in the bandgap [12][13][14].…”

On the Bending and Vibration Analysis of Functionally Graded Magneto-Electro-Elastic Timoshenko Microbeams

“…This MCST and its extended versions only consider the symmetrical part of the curvature tensor, which leads to fewer material parameters than their classical counterparts. In view of the great difficulties for determining additional parameters and interpreting the relevant microstructures, these modified theories have been applied to build micro/nano-beam and periodic composite pipe models [36][37][38][39][40][41], from which a microstructure-dependent stiffness is revealed. Recently, three such models have been proposed for MEE Timoshenko homogeneous beams [39] and MEE homogeneous plates [42,43] based on the extended modified couple stress theory.…”