The paper proposes a method to solve the problem of vibrations of a radially polarized piezoelectric cylinder subject to nonstationary electric excitation. The dynamic electromechanical state of the cylinder is analyzed. The time-dependences of electric and mechanical characteristics are plotted. The distribution of these characteristics over the cross section of a short cylinder is examined. The region of end disturbances in a long cylinder is identified
The paper proposes and analyzes different approaches to constructing numerical schemes to solve the nonstationary vibration problem for a radially polarized piezoelectric hollow cylinder with different electric boundary conditions under mechanical loading. It is established that when the cylinder is subjected to internal pressure, the radial displacements are similar and the longitudinal displacements substantially different in cylinders with electroded and nonelectroded surfaces Keywords: piezoelectric hollow cylinder, nonstationary vibrations, numerical schemes, internal pressure Introduction. The widespread use of miscellaneous piezoelectric transducers [3, 10, etc.] necessitates studying the dynamic behavior of structural members made of piezoceramic materials. The harmonic electroelastic vibrations of piezoceramic bodies were studied in [3, 7, 11, 17, etc.]. The vibrations of piezoceramic rods under shock loading were addressed in [4,5]. Two-dimensional nonstationary problems of electroelasticity were solved in [6,9]. The nonstationary electroelastic acoustic vibrations of piezoceramic shells and cylinders in hydraulic systems were studied in [1, 2, 13].We will use direct integration to solve the initial-boundary-value vibration problem for a radially polarized hollow piezoceramic cylinder under mechanical loading. Different electric boundary conditions will be examined. Integration over time will be carried out using explicit and implicit schemes and the Runge-Kutta method, and the corresponding results will be compared.1. Problem Formulation. Consider a radially polarized hollow piezoceramic cylinder with mid-surface radius R, thickness 2h, and length l described in a cylindrical coordinate frame r z , , q . The end z = 0 of the cylinder is rigidly fixed. The
A numerical algorithm for analyzing the planar nonstationary axisymmetric vibrations of piezoceramic circular plates polarized across the thickness and subject to electric excitation is developed. The dynamic characteristics of a ring plate are analyzed. The dependence of the behavior of its nonstationary vibrations on the frequency of the instantaneously applied electric potential and the ratio of outer and inner radii is established Keywords: piezoelectric ring plate, nonstationary electroelastic vibrations, electric excitation, numerical methodIntroduction. Piezoelectric plates are the most widespread electromechanical transducers operating within a wide frequency range under impulsive electric and mechanical excitation [2, 5, 8, 15, 16, etc.]. Experimental and theoretical studies of their dynamic characteristics are reported in numerous scientific publications, which are mainly focused on stationary harmonic vibrations and resonant frequencies [1, 2, 9, 13, 14, etc.]. Aspects of the nonstationary vibrations of circular disks were analyzed in [3,11] regardless of the coupling of the fields. The vibrations of piezoceramic bodies polarized across the thickness and subjected to nonstationary loads were studied in [6,7,10,12], naturally neglecting the influence of the in-plane configuration of transducers on the wave processes. For thin transducers, this omission can be remedied by considering the plane stress state and linear distribution of electric potential over the thickness [1,2,4,6,15]. We will use such a problem statement to study the dynamic axisymmetric electromechanical state of thin circular piezoceramic plates polarized across the thickness and subjected to electric excitation. Three numerical algorithms will be analyzed.
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