Determination of electrical impedance of piezoceramic disk and its calculation in medium and high frequency regions

The final goal of mathematical modeling of physical condition of vibrating piezoelectric elements is a qualitative and quantitative description of characteristics and parameters of existing electrical and elastic fields. It is clear that to obtain meaningful and reliable quantitative estimates of physical condition parameters of piezoelectric (piezoceramic) element is not possible without reliable data on the values of physical and mechanical constants of the materials. Thus, it is necessary to build noncontradictory method of material constants experimental determination of piezoelectric ceramics, which delivers reliable values of at least three modules of elasticity, two elements of the matrix of piezoelectric coefficients and one element of the matrix of dielectric constants, which is the purpose of the work. The main results of this paper can be written as follows: – at sufficiently general initial assumptions a mathematical description of electrical impedance of oscillating thin piezoceramic disk with end surfaces continuous covering by electrodes in vacuum is obtained; – the expression for electrical impedance calculating of oscillating piezoceramic disk at middle frequencies is built, where the vector of disk’s material particles displacement is almost completely determined by radial component; – with the help of the averaging method a system of differential equations in partial derivatives is solved, and on this basis, a mathematical model of electrical impedance of piezoceramic disk at high frequencies is built, where the vector of material particles displacement is determined by radial and axial components