Elastic wave band gaps in magnetoelectroelastic phononic crystals

In this paper, the elastic wave propagation in two-dimensional magnetoelectroelastic phononic crystals is studied taking the magneto–electro–elastic coupling into account. The electric and magnetic fields are approximated as quasi-static. The band gap characteristics for three kinds of lattices (i.e. regular triangle, square and hexagon) are investigated by the plane-wave expansion method. Regarding the variables of mechanical, electrical and magnetic fields as the elements of the generalized state vector, the expression of generalized eigenvalue equation is derived. Numerical results are presented for BaTiO3–CoFe2O4/polymer composite. From the results it can be observed that the band gap width can be changed by lattice shape and corresponding filling fraction. Compared with the first band gap, the second and third ones are wider for hexagonal lattice. The piezoelectricity and piezomagneticity have significant effects on characteristics of the second band gap, especially for larger filling ratios. For the first band gap, however, the differences are not obvious between the cases with and without considering the piezoelectric and piezomagnetic constants.