Resonant electromechanical vibrations of piezoelectric shells of revolution (review)

Abstract

Scientific results from studies on the resonant electromechanical vibrations of piezoceramic thin-walled shells of revolution, their fragments, and segmented cylinders are analyzed, systematized, and generalized. Considerable attention is focused on experimental studies of resonant vibrations. It is shown that the modes in which deformation occurs inphase throughout the volume are of the highest intensity in all piezoceramic shell structures Introduction. The modern piezoelectric transducers employ either direct or converse piezoeffect, or both, as in piezoelectric transformers, i.e., piezoelectric bodies convert electrical energy into mechanical or, vice versa, mechanical energy into electrical. The efficiency of piezoelectric energy conversion is determined by the static and dynamic electromechanical-coupling coefficients and the intensity (amplitude) of mechanical vibrations relative to the level of the applied electric power. The papers [39,91] present and analyze the results from the author's long-term research into the resonance vibrations of thin piezoelectric plates and outline the fundamentals of an experimental technique for frequency measurement and application of the efficient piezotransformer transducer (PTT) method to the study of the planar vibrations of piezoceramic plates.In the last decades, piezoelectric, primarily ceramic shells of various geometries have been widely used in vibration detection and control systems, such as sensors and actuators, and in multilayer metal-ceramic structures. Research into the resonant electromechanical vibrations of piezoceramic shells of revolution is a task of current importance in the mechanics of coupled fields in materials and structural members.The present paper is concerned with the resonant electromechanical vibrations of piezoelectric shells of revolution and compound segmented bodies under electric loading and is based on the author's publications over the last 30 years. Considerable attention will be given to experimental methods for studying resonant vibrations and to their results. It will be shown that when applied to piezoceramic shells of revolution, the piezotransformer transducer method measures the sum of principal mechanical stresses and does not sense bending moments. We will analyze experimental data on the stationary vibrations and stress state of and the efficiency of electric-to-mechanical energy conversion by monolithic and segmented piezoceramic shells of revolution in the form of a cylinder, a sphere, and a truncated cone described in [13, 20, 26-29, 31-36, etc.]. The experimental studies to be reviewed were carried out using either standard procedures [2,15,17,18,51,58,77] or the PTT method [22,26,[91][92][93][94], which makes it possible to analyze the stress state and to measure the components of mechanical energy losses [5,24,30,31,36,38,39]. Brief Review of Publications on the Resonant Vibrations of Piezoceramic Shells of Revolution.The piezoceramic technology allows producing specimens of any geometry and dimensions. In this resp...

Resonant frequencies of electroelastic vibrations of piezoceramic plates

“…Piezoelectric circular thin-walled elements are used in various ultrasonic devices. The axisymmetric radial vibrations of thin piezoceramic disks and ring plates with thickness polarization were studied in many publications [1,4,5,7,8,10,11,13,14] beginning with [12]. However, no systematic analysis of the influence of the boundary conditions on the resonant frequencies has been performed.…”

“…In the axisymmetric plane case, of the three vibration equations in cylindrical coordinates, only the following is used [6,8] [6] in terms of first-order cylindrical Bessel functions of the first and second kinds: …”

Electromechanical vibrations of a piezoceramic hollow spheroid with a polar notch

“…The test specimen is made by joining a spherical shell and a cylinder. We will also use the piezotransformer transducer method (PTTM) repeatedly described in the literature [2,3,7,11]. In particular, it will be shown that the deformation of the spheroid is asymmetric at all strong resonances, even though the specimen is geometrically axisymmetric.…”

“…The electromechanical vibrations of spherical and spheroidal piezoceramic structures, including a cylinder joined to a closed spherical shell or to an open spherical shell (made by removing a cylindrical portion from a compound spheroid) were studied on [11]. Comparing Figs.…”

“…The The above frequencies can be used to calculate the squared electromechanical-coupling coefficients by the following well-known formula [11]: …”