About natural frequencies and forms of electroelastic vibrations of ring piezoceramic plates

DOI: 10.31673/2412-9070.2023.046070

Abstract

The general solution of problem non-axisymmetric electromechanical vibrations of piezoceramic ring plate is obtained. For the plates with radial cuts of electrode covering and for boundary conditions rigid clamping — free edge, free edge — rigid clamping the spectra of natural frequencies of vibrations are mode shapes for the first harmonics in the circumferential coordinate are identified are numerically determined and analyzed. The comparative analysis of natural frequencies and forms of piezoelectric vibrations of polarized on thickness ring piezoceramic plates is executed under various boundary conditions. One of the important characteristics of the forms of oscillations is the number and location of nodal lines. From the obtained results for the frequency equations and asymptotic formulas for frequencies, it follows that the number of nodes and the nature of the forms under all types of boundary conditions can be determined by the asymptotic approximation. Under different boundary conditions, an integer number of half-waves can be placed on the width of the ring (the forms n = 1,2,3,4 at have the number of nodes n –1); or an odd number of quarter waves is placed on the width of the ring (forms have the number of nodes); or an odd number of quarter waves is placed on the width of the ring (forms have the number of nodes); or an integer number of half-waves is placed on the width of the ring (forms have the number of nodes). These findings are better confirmed for natural frequencies and forms with higher numbers.

Keywords: piezoceramic ring plate; radial cuts of electrode covering; non-axisymmetric electromechanical vibrations; spectra of natural frequencies.

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