Dynamic Electromechanical Coupling Coefficient Research Articles

Effect of Split or Partial Electrodes on the Forced Vibrations of Bar-Type Piezoceramic Transducers

The effect of a nonuniform electric load on the admittance and dynamic electromechanical coupling coefficient (EMCC) of energy converters is analyzed using, as examples, well-known problems of the forced vibrations of narrow piezoceramic plates with partial or split electrodes. It is shown that the antiphase excitation of vibrations can be effective to extract harmonics and to increase the operating frequencies of resonators. The presence of unelectroded sections can result in some increase in the EMCCof the principal resonance. If some electrodes are short-circuited, then odd and even longitudinal modes can be excited, which are absent when the electrodes are not split. The calculation of the stress state and admittance is in good agreement with experiments

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

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

Resonant frequencies of electroelastic vibrations of piezoceramic plates

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

A model of bending vibrations of piezoelectric bimorphs with split electrodes and its applications

We study stationary vibrations and static bending of a bimorph plate consisting of two piezoceramic layers with an infinitely thin split electrode between them. We propose a model taking into account the square root singularity of the electric field structure on the interface between the split electrode regions. For the plane problem, we obtain the equation of motion and formulate the boundary conditions and the transmission conditions on the interface between the split electrode regions. For the piezoceramic PZT-4, we calculate the resonance and antiresonance frequencies and study the dependence of the dynamic electromechanical coupling coefficient on the dimensions of the internal electrode. We show that the use of a plate with a split electrode permits increasing the efficiency of vibration excitation compared with the case of a solid internal electrode. In the case of static bending of the plate-strip, we determine the dimensions of the internal electrode ensuring a significant increase in the deflection at the center of the bimorph.

The influence of electrode designs on the resonant vibrations for square piezoceramic plates

In this paper, the resonant vibrations of square piezoceramic plates with four different electrode designs are investigated. Two experimental techniques, the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and the impedance analysis, are used to access the influence of the electrode arrangement on the resonant characteristics of square piezoceramic plates. Both the out-of-plane and in-plane resonant frequencies and full-field mode shapes of piezoceramic plates with various electrode designs are obtained from the AF-ESPI method. The impedance analyzer is used to measure the resonant and antiresonant frequencies of piezoceramic plates. The dynamic electromechanical coupling coefficient (EMCC), which relates to the ability of conversion between mechanical and electrical energy, is determined from the measured values of resonant and antiresonant frequencies. Experimental results of the resonant vibration characteristics of the square piezoceramic plates are verified by numerical computations based on the finite-element method. Excellent agreement between the experimental and numerical results is found in resonant frequencies and corresponding mode shapes. It is found that the electrode design has important influence on the resonant characteristics of piezoceramic plates. The effect of different designs of electrode is more significant in the in-plane modes than that in the out-of-plane modes.

Analysis of Natural Vibrations of Round Flexing Membrane-Type Piezoelectric Transducers with an Arbitrary Dimension Ratio

The problem of natural vibrations of a round exing membrane-type piezoelectric transducer (piezoelectric plate) with an arbitrary dimension ratio is solved in the exact formulation using the finite element method for two variants of fastening the membrane (simply supported and rigidly fixed plate). The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distributions over the plate surfaces are also analyzed and the dependences of the dynamic electromechanical coupling coefficient are investigated as functions of the geometric dimensions of the piezoelectric transducer, the plate material, and the piezoelectric ceramic composition. The optimum geometric dimensions of the transducer which ensure the maximum dynamic electromechanical coupling coefficient are determined and the value of the coefficient is estimated.

Analysis of the natural vibrations of circular piezoceramic plates with partial electrodes

The finite-element method is used to analyze the thickness-symmetric vibrations of piezoelectric plates with partial electrodes. The spectra of the natural vibrations at resonance and antiresonance, the dynamic electromechanical coupling coefficient, and the vibration modes of these plates are studied for a wide range of geometric dimensions of both the plates and the partial electrodes. The optimal dimensions of the plates and electrodes, which correspond to the maximal values of the coupling coefficient, are determined. The increase in the coupling coefficient due to the utilization of the partial electrodes is considered for piezoelectric plates made of ceramics of various compositions. It is shown that all piezoceramic compositions can be divided into two groups. For the first group, the utilization of the partial electrodes can increase the coupling coefficient of the thickness vibrations by 7–23%, depending on the vibration mode. For the second group of piezoceramics, the coupling coefficient cannot be increased in this way; in other words, complete electrodes are optimal for the thickness vibrations of plates made of piezoceramics that belongs to the second group.

Analysis of Natural Vibrations of Round Bimorph Piezoelectric Ceramic Plates of Arbitrary Dimensions. I. Simply Supported Piezoelectric Plate

The problem of natural vibrations of a round bimorph rigidly fixed supported piezoelectric ceramic plate (piezoplate) of an arbitrary thickness with arbitrary axisymmetric electrodes is solved using the method of finite elements. The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distributions over the piezoplate surfaces (vibration modes) are also analyzed and the dynamic electromechanical coupling coefficient (DCC) is investigated as a function of the relative plate thickness for various piezoelectric ceramic compositions. Round bimorph piezoplates with partial electrodes are considered; it is shown that the DCC can be significantly (by tens times) raised using partial electrodes. The results obtained make it possible to estimate the limits of applicability of the approximate one-dimensional theory and choose the optimum geometric dimensions of the plate and electrodes that ensure the maximum DCC.

A general approximated two-dimensional model for piezoelectric array elements

In this paper we describe an approximate two-dimensional model of a single piezoelectric array element. Substantially, the element is a two-dimensional structure whose vibrations can be described by two coupled differential wave equations with coupled boundary conditions. We take as a solution of this system two orthogonal wave functions which depend only on one axis, corresponding to the propagation direction, and which satisfy the boundary conditions only in an integral form. This solution makes it necessary to neglect the piezoelectric coupling in the transverse direction; nevertheless this approximation does not substantially affect the computed results because the transverse elastic coupling is much stronger than the piezoelectric one. With our model, the external behavior of the element in the frequency domain can be described by a 5/spl times/5 matrix from which all the transfer functions of the element can be easily computed. We compared our results with those of the classical Mason-Sittig one dimensional model, finding, as expected, a small difference in the principal thickness resonance frequency and the presence of a lateral mode. To verify the results obtained with our model, we computed the frequency spectrum of the element varying the width/thickness ratio. We found a good agreement with the low branch of the spectrum computed by the coupled mode theory. Finally, we computed, in the frequency domain, the dynamic electromechanical coupling coefficient k/sub U/, evaluating the internal energy distribution of the element and applying the definition reported by Berlincourt. We compared the values at resonance with the appropriate quasistatic coupling factors k/sub 33/' and k/sub 31/' and with the effective coupling factor k/sub eff/ computed by the same model. >

Mode theory of electromechanical energy conversion in piezoelectric materials

The method of eigenfunctions is generalized to the problem of dynamic electroelasticity /1/, which allows of a larger variety of physically realisable boundary conditions. Using the method of eigenfunctions a so-called mode theory of electromagnetic energy conversion is developed. Its basic idea is the establishment of a connection between the dynamic electromechanical coupling coefficient of the specified displacement field and the mode or partial electromechanical coupling coefficients of the individual modes of oscillation. The latter, being non-linear integral characteristics of normal modes, play the same fundamental role with respect to the first as the eigenfunctions (normal modes) play with respect to the overall solution of the electro-elasticity problem. The coefficients of the expansion in eigenfunctions of the displacement field which gives a maximum permissible value of the electromechanical coupling coefficient for a given geometry, position of the electrodes, and method of supplying and removing the electrical energy.