One-dimensional equations for piezoelectromagnetic beams and magnetoelectric effects in fibers

We derive one-dimensional equations for the extension and flexure with shear deformation of a piezoelectromagnetic beam with rectangular cross section from three-dimensional equations. The equations obtained are used to analyze magnetoelectric effects in fibers of piezoelectric/piezomagnetic composites. Both static magnetoelectric effects and frequency-dependent magnetoelectric effects in time-harmonic motions are examined. Various material and field orientations are considered. We also make comparisons between magnetoelectric effects in fibers and in thin films on substrates. Two-dimensional equations for laminated piezoelectric/piezomagnetic plates are used in the analysis of the thin films. It is found that magnetoelectric effects in fibers are significantly stronger than those in thin films on substrates.