THE NONSTATIONARY AXISYMMETRIC PROBLEM OF ELECTROELASTICITY FOR A THICK CIRCULAR ANISOTROPIC PIEZOCERAMIC PLATE

anisolropic piezoceramic plate (short continuous cylinder). The plate is axially polarized and acted upon by hard normal stresses which are arbitrary functions of the radial coordinate and time. The case is investigated where the end surfaces of the plate are equipped with electrodes which are connected to a sensitive measuring device with a substantial input resistance, whereas the curved lateral surfaces are free from electrodes. This case is of practical importance for devices of direct piezoelectric effect with a piezoceramic element in the form of a plate. In this case, the plate operates in the conditions close lo no-load [I]. For an axially polarized plate, there are no free charges on the curved and end surfaces of the plate. A new closed-form solution is obtained using the method of expansion in the vector eigenfunctions [2] in the form of the sinictural algorithm of finite integral transforms (FIT) [3, 4]. The natural vibration frequencies, displacements, and intensity of the induced electric field are analyzed. Solving initial-boundary value problems of electroelasticity for finite plates in the three-dimensional formulation leads to considerable difficulties. For this reason, these problems were considered with kinematic hypotheses adopted in [he engineering theory in (he case where only mechanical or electric disturbances act on the system [5-9]. An exact solution of the problem ofelectroelasticity for nonstationary torsional vibrations of a finite nonhomogeneous cylinder is constructed in [10] using the FIT method. Also, approximate solutions of the dynamic problems for the direct and inverse piezoelectric effect in terms of finite differences are available for a piezoceramic cylinder with a radial [11] and axial [12] polarization.