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

Theoretical Investigation of Magneto-Electro-Elastic Piezoelectric Phononic Crystal

We design a magneto-electro-elastic piezoelectric phononic crystal (MPPC) using a one-dimensional piezoelectric superlattice (with a 3m point group) and split-ring resonators. The effect of the split-ring resonators is to enhance the piezoelectric effect of the piezoelectric superlattices. This effect will create elastic anomalies and generate the phononic band gaps. These are first proposed theoretically. We calculate the transmission function of the MPPC through Transfer Matrix Method of the phononic crystal. By using the transmission function, we theoretically study the propagation properties of the acoustic waves in the MPPC. The mechanism for multifield coupling is analyzed. A type of phononic band gap is created, called the multifield coupling phononic band gap. We analyze the possibility of crystals as left-handed metamaterials. We also discuss some potential applications.

Dispersion Diagram of Trigonal Piezoelectric Phononic Structures with Langasite Inclusions

The dispersion relation of elastic Bloch waves in 1-3 piezoelectric phononic structures (PPnSs) with Langasite (La3Ga5SiO14) inclusions in a polymeric matrix is reported. Langasite presents promising material properties, for instance good temperature behaviour, high piezoelectric coupling, low acoustic loss and high quality factor. Furthermore, Langasite belongs to the point group 32 and has a trigonal structure. Thus, the 2-D bulk wave propagation in periodic systems with Langasite inclusions cannot be decoupled into XY and Z modes. The improved plane wave expansion (IPWE) is used to obtain the dispersion diagram of the bulk Bloch waves in 1-3 PPnSs considering the classical elasticity theory and D3 symmetry. Full band gaps are obtained for a broad range of frequency. The piezoelectricity enhances significantly the band gap widths and opens up a narrow band gap in lower frequencies for a filling fraction of 0.5. This study should be useful for surface acoustic wave (SAW) filter and 1-3 piezocomposite transducer design using PPnSs with Langasite.