Piezoelectricity, its history and applications

The three-dimensional equations of electroelasticity in Cartesian, cylindrical, and spherical coordinates are represented in Hamiltonian form with respect to the thickness coordinate. The boundary-value problem with a harmonic potential difference and zero mechanical load given on the boundaries is solved numerically. The amplitude-frequency characteristics and natural frequencies are compared. The resonant and antiresonant frequencies of the current and the dynamic electromechanical coupling coefficient are determined Keywords: piezoelectric layer, sphere, plate with transverse polarization, electroelastic thickness vibrations, amplitude-frequency characteristics, resonant and antiresonant frequencies Introduction. Piezoelectric elements (plates, cylinders, spheres, etc.) are widely used in various devices [1,3,9]. The study of their dynamic characteristics is of scientific and applied importance. The exact analytic solution describing the thickness vibrations of a plate-like vibrator is well known [1, 6, etc.], whereas the analytic solutions for cylindrical and spherical vibrators with arbitrary boundary conditions are formal because they require evaluating integrals of special functions. When curvature is small, it is expedient to seek solutions in the form of ordinary power series of linear functions of the radial coordinate. This approach was followed to solve many problems of wave propagation and vibration in elastic and piezoelectric cylindrical and spherical bodies [6, 10 11]. The electroelastic vibrations of cylinders were studied using the variational difference and finite-element methods [6, etc.]. The method of lines and spline functions (for approximation in one coordinate) were used in [7,8] to study the vibrations of electroelastic cylinders. The problems addressed in these papers were partially solved earlier, but no comparison with their solutions was made. As for the accuracy of the solutions, no particulars were given in [7,8], just generalities.The present paper outlines a unified approach to the solution of the problem for a plate, a cylinder, and a sphere. We will reduce the three-dimensional equations of electroelasticity to an operator Hamiltonian system with respect to the thickness coordinate and analyze the properties of this system. In the case of a harmonic electric potential, we will numerically determine the amplitude-frequency characteristics, resonant and antiresonant frequencies, and dynamic electromechanical-coupling coefficient. The results will be subject to comparative analysis.1. Problem Formulation. To study the harmonic electroelastic vibrations of a piezoelectric plate, cylinder, and sphere, we will start with the equations of mechanical vibrations [6]

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“…These frequencies are called antiresonant frequencies [6,9]. In the above problems, they can be found from…”

Section: Calculated Results and Their Analysismentioning

confidence: 99%

“…Piezoelectric elements (plates, cylinders, spheres, etc.) are widely used in various devices [1,3,9]. The study of their dynamic characteristics is of scientific and applied importance.…”

mentioning

confidence: 99%

Comparative analysis of the electroelastic thickness vibrations of layers with curved boundaries

Shul’ga

Grigor’eva

2011

Int Appl Mech

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“…Disk-and ring-shaped vibrators with solid electrodes on the faces undergo axisymmetric vibrations [4,9]. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Levchenko

2015

Int Appl Mech

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“…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.…”

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confidence: 99%

Resonant frequencies of electroelastic vibrations of piezoceramic plates

2011

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The harmonic electroelastic vibrations of a thin ring plate are considered. The effect of boundary conditions on the natural frequencies is studied. The asymptotic properties of the frequency spectrum are determined. The dependence of the resonant and antiresonant frequencies and the dynamic electromechanical-coupling coefficient on the relative size of plate is analyzed Keywords: piezoceramic plate, resonant and antiresonant frequencies, asymptotics of frequency spectrum Introduction. 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. This issue is discussed in the present paper.We will establish the asymptotic properties of the frequency spectrum and will show that they can be determined with an admissible error by simple asymptotic formulas even at low frequencies. We will also ascertain which boundary conditions correspond to a more rigid mechanical system. The dependence of the resonant and antiresonant frequencies and the dynamic electromechanical-coupling coefficient (EMCC) on the relative size of the plate will be analyzed.1. Problem Formulation. Consider a thin piezoceramic plate of thickness h. We choose a cylindrical coordinate system Or z q with the plane z = 0 coinciding with the midsurface of the plate. If the plate has thickness polarization and undergoes

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Piezoelectricity, its history and applications

Cited by 28 publications

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Comparative analysis of the electroelastic thickness vibrations of layers with curved boundaries

Comparative analysis of the electroelastic thickness vibrations of layers with curved boundaries

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

Resonant frequencies of electroelastic vibrations of piezoceramic plates

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