Harmonic oscillations of a piezoceramic functional-graded sectional cylinders with account of energy dissipation

Abstract

Harmonic oscillations of piezoceramic functional-gradient sectioned hollow cylinders are studied, taking into account energy dissipation. A cylinder of finite length is considered, consisting of an even number of sections polarized in the circular direction, which are connected to each other by similar sides. The material is considered to be functionally heterogeneous in the direction of the previous polarization. The cylinder is loaded by the potential difference applied to the flat faces of the sections. The calculation is performed by the finite element method. The forming of damping matrix and determining the coefficients corresponding to the four ways of introducing Rayleigh damping into the FEM is described. Amplitude-frequency responses taking into account damping are built for displacements, charge on the electrodes, electrical admittance and its logarithm. The consideration of energy dissipation according to the Rayleigh damping model is related to the experimental data due to the Q factor of the piezo element. The frequencies of electrical resonances, anti-resonances and the corresponding electromechanical coupling coefficients for functionally inhomogeneous and homogeneous cylinders are determined. For the functional-gradient piezoelectric element of the considered configuration, the maximum CEMC occurs at the frequency of the second electrical resonance. At this frequency, the dynamic stress-strain state of the cylinder is investigated. Forms of oscillations and distribution of stress amplitude values are constructed. The largest normal stresses according to the Coulomb-Mohr strength theory are determined and compared with the von Mises strength theory. FEA allows three-dimensional calculation of harmonic oscillations of functional-gradient piezo elements of complicated geometry. The determined frequencies of electrical resonance and anti-resonance and the corresponding CEMC make it possible to choose the most effective operating mode of the piezo element. The FEM mathematical apparatus makes it possible to quickly and qualitatively evaluate the strength, determine the charge on the electrodes, the current in the circuit, build the amplitude-frequency characteristics of admittance and impedance, and evaluate the efficiency of energy conversion.