Flexural Vibrations of a Composite Piezoactive Bimorph in an Alternating Magnetic Field: Applied Theory and Finite-Element Simulation

An applied theory describing the transverse vibrations of a cantilever bimorph in an alternating magnetic field is presented. The bimorph is made of piezoactive materials, which is a multilayer composite with alternating piezoelectric and piezomagnetic layers. The mechanical and physical properties of such a composite are specified by their effective constants. This theory can serve as a model for energy harvesting devices under the action of an external alternating magnetic field. Within the framework of the theory, quadratic distributions of electric and magnetic potentials over the cantilever thickness are assumed inhomogeneous in its longitudinal direction. The stress-strain state of the bimorph, the distribution of electric and magnetic fields, and its natural frequencies are calculated. In addition, the case where the potential at one of electrodes is unknown is examined. The results of calculations in the low-frequency region are compared with those found by a finite-element model based on a system of partial differential equations built in the COMSOL Multiphysics package. A comparison showed a good agreement between the calculated field characteristics and the data of finite-element modeling in the entire area of the bimorph, except in the vicinity of the beam fixation and its free end.