Propagation of axial shear magneto–electro-elastic waves in piezoelectric–piezomagnetic composites with randomly distributed cylindrical inhomogeneities

The integral equations of the scattering problem for piezoelectric–piezomagnetic composites with an inhomogeneity are derived. In the long-wave limit, the solutions of these integral equations for the composites containing a single inhomogeneous fiber are solved in close forms. The total scattering cross-section for the one-fiber composites is also obtained. By the so-called effective field method, the multi-fiber scattering problem is simplified to the one-fiber scattering problem, and the analytical expressions of magneto–electro-elastic fields for the multi-fiber composites are obtained in the long-wave limit. These solved magneto–electro-elastic fields are then used to solve the expressions of the static effective moduli, effective wave velocity and attenuation factor of piezoelectric–piezomagnetic composites with randomly distributed cylindrical inhomogeneities. Through numerical examples, it concludes that, if the random set of fiber cross-sections is homogeneous and isotropic, the effective field method is coincident with the Mori–Tanaka mean field method when the static effective moduli of piezoelectric–piezomagnetic composites are looked for. Moreover, the rules of the effective wave velocity versus the volume fraction of fibers are investigated for specific materials.