On the longitudinal wave along a functionally graded magneto-electro-elastic rod

We consider a functionally graded magneto-electro-elastic rod made of piezoelectric BaTiO3 and piezomagnetic CoFe2O4. The materials properties are assumed to vary exponentially along the rod direction. We derive the one-dimensional wave-motion equation for the functionally graded magneto-electro-elastic rod. Furthermore, for this one-dimensional problem, we demonstrate the phase velocity and frequency spectrum, and discuss the important influence of the gradient factor as well as material coupling on the wave features. We also calculate and compare the effective Young’s modulus and effective Poisson’s ratio in the BaTiO3- CoFe2O4 composite rod made of different volume fractions of BaTiO3, showing clearly the important effect of the material coupling on these parameters.