Numerical solution to the initial-boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder

Abstract

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

Electroelastic two-dimensional nonstationary vibrations of a piezoceramic prismatic body under mechanical loading

“…The one-dimensional nonstationary vibrations of piezoelectric bodies subject to dynamic electric and mechanical excitation were addressed in [1,2,4,5,15,18,19]. Numerical approaches to solving two-dimensional initial-boundary-value problems of electroelasticity were proposed in [6,9,13,14,16].In the present paper, we develop a numerical method to solve the plane problem of electroelasticity for a prismatic piezoceramic body with rectangular cross-section under mechanical loading and analyze its dynamic electromechanical state depending on the geometrical and mechanical parameters. …”

“…The one-dimensional nonstationary vibrations of piezoelectric bodies subject to dynamic electric and mechanical excitation were addressed in [1,2,4,5,15,18,19]. Numerical approaches to solving two-dimensional initial-boundary-value problems of electroelasticity were proposed in [6,9,13,14,16].…”

Method of characteristics in analysis of the propagation of electroelastic thickness oscillations in a piezoceramic layer under electric excitation

“…Thus, problem (1)-(4) is reduced to problem (5), (11) with initial conditions (4). Substituting (7) into the first boundary condition in (11), we obtain f c t g c t ( ) ( )…”

Vibrations of a piezoceramic cylinder subject to nonstationary electric excitation

“…Other types of loading are addressed in [2,13]. Let us nondimensionalize the complete system of electroelasticity equations (1.1)-(1.4) and the boundary conditions (1.6), (1.7) by changing variables as follows: where r 00 , c 00 , e 00 , and t h c h = r 00 00 / are normalizing coefficients.…”

“…A comparative analysis of the solutions was performed in [13]. = S , and r r 00 = , which are used to nondimensionalize (1.9).…”