Applied Theory of the Vibration of Inhomogeneously Polarized Axisymmetric Bimorph Piezoelements

Abstract

Piezoelectric generators (PEG) are effective for energy harvesting in machines vibrating elements. Using inhomogenously polarized piezoelements in PEG allows one to increase its output characteristics (output electric potential and output power). The paper considers piezoelements, which are circular multilayer plates (bimorphs), consisting of piezoceramic layers with inhomogeneous polarization (in thickness and in radial direction). Such a method of polarization makes it possible to use a piezomodule d33 for bending vibrations, which is significantly larger than piezomodule d31. PEG optimization can be performed on the base of mathematical modeling of the process. Linear electroelastic theory, implemented in ACELAN and ANSYS software, was used as mathematical model. Moreover, the applied theory of axisymmetric bending vibrations with a piecewise constant polarization was created. In the applied theory, hypotheses about the distribution of displacements and electric potential along the thickness of the piezoelectric element have been adopted. System of ordinary differential equations and boundary conditions for steady bending vibrations for deflection and electric potential, depending on the radial coordinate, has been formulated. A series of calculations was performed in which resonance frequencies, antiresonance and output characteristics of PEG were determined depending on the design parameters.