Electrically Excited Nonstationary Vibrations of Thin Circular Piezoelectric Plates

Abstract

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.

Effect of Boundary Conditions on the Natural Frequencies and Vibration Modes of Piezoelectric Plates with Radially Cut Electrodes

“…The natural frequencies of electroelastic radial vibrations (11) are analyzed in [12]. Azimuthal vibrations (11), which cannot be excited electrically, are addressed for a fuller analysis of the results.…”

“…When N = 0 (axisymmetric vibrations) and one (inner or outer) of the edges is clamped (boundary conditions (12) and (13)), the second, fifth, and seventh frequencies represent radial vibrations (10) and the first, third, fourth, and sixth frequencies represent azimuthal vibrations (11). When the edges are free, the first, third, and sixth frequencies represent radial vibrations and the second, fourth, fifth, and seventh frequencies represent azimuthal vibrations.…”

“…When the edges are free, the first, third, and sixth frequencies represent radial vibrations and the second, fourth, fifth, and seventh frequencies represent azimuthal vibrations. When one edge is clamped (boundary conditions (12) and (13)), the natural frequencies approach each other with increasing mode number. This is also true for the boundary conditions (14) (free edges), but the associated frequencies are lower.…”

“…The vibrations will be nonaxisymmetric with respect to the circumferential coordinate if the electroelastic sectors of a ring plate with radially cut electrodes are excited in antiphase. The circumferential vibration modes and the associated frequencies are determined by the number of radial cuts in the electrodes [2,3,11,12]. Here we will compare the frequency spectra of a plate with boundary conditions of three types.…”

Measuring the Amplitudes and Phases of Vibrations of Piezoceramic Structural Elements

“…It appeared that the presence or absence of nonlinearity mentioned in [27][28][29] is due to an increase or a decrease in instantaneous power as a resonance is approached. However, this is beyond the scope of the present paper and should be studied separately.…”