Mode excitation efficiency for contour vibrations of piezoelectric resonators

This paper addresses a theoretical procedure for control of the contour mode excitation efficiency in thin piezoelectric arbitrarily-shaped resonators by adjusting the surface electrode configuration to the mechanical stress distribution. The procedure allows accurate determination of at least five efficiently excited modes for various electrode configurations. This is validated by experimentally measured data for rectangular resonators. For the first time, electrode configurations are suggested that provide high values of the dynamic electromechanical coupling factor for the longitudinal edge mode in a rectangular resonator, while the excitation of spurious modes is suppressed.     

Analysis of nonlinear transient responses of piezoelectric resonators

The electric transient response method is an effective technique to evaluate material constants of piezoelectric ceramics under high-power driving. In this study, we tried to incorporate nonlinear piezoelectric behaviors in the analysis of transient responses. As a base for handling the nonlinear piezoelectric responses, we proposed an assumption that the electric displacement is proportional to the strain without phase lag, which could be described by a real and constant piezoelectric e-coefficient. Piezoelectric constitutive equations including nonlinear responses were proposed to calculate transient responses of a piezoelectric resonator. The envelopes and waveforms of current and vibration velocity in transient responses observed in some piezoelectric ceramics could be fitted with the calculation including nonlinear responses. The procedure for calculation of mechanical quality factor Q(m) for piezoelectric resonators with nonlinear behaviors was also proposed.     

Measurement of piezoelectric modulus by pulsed excitation of piezoelectric ceramic elements

The possibility of measuring the piezoelectric modulus by exciting piezoelectric ceramic components with a radio pulse is considered. It is shown that there is a relation between the piezoelectric modulus and the rate of change of the current envelope at the beginning of the transient. Theoretical relations are derived. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 71–72, October, 2006.     

计及压电效应时矩形振子的三维振动研究

在计及压电效应的情况下，本文利用解析方法对有限尺寸压电陶瓷矩形振子的三维振动进行了研究，推出了振子耦合振动的频率方程，并对振子的振动模式进行了分析。理论研究表明，利用本文中的解析法研究振子的耦合振动，计算简单、物理意义明显。与传统的一维理论分析方法及数值方法相比，由于本研究考虑了振子的压电效应以及不同振动模式不同的相互耦合，因此，振子的理论计算频率与测量值更加符合。     

Random excitation of nonlinear elastic structures with internal resonances

The influence of random vibration on the design of mechanical components has been restricted to the linear theory of small oscillations. However, this theory is inadequate and fails to predict the complex response characteristics which may be observed experimentally and can only be predicted by employing the nonlinear theory. This paper presents a brief overview of the basic nonlinear phenomena associated with nonlinear random vibration. An example of a clamped-clamped beam under filtered white noise excitation in the neighbourhood of 1:1 internal resonance condition is considered. Three approaches are employed to examine the response and stochastic bifurcation of the beam coupled modes. These are the Fokker-Planck equation together with closure schemes, Monte Carlo simulation, and experimental testing. The analytical results are compared with those determined by Monte Carlo simulation. It is found that above a critical static buckling load the analytical results fail to predict the snap-through phenomenon, while both Monte Carlo simulation and experimental results reveal the occurrence of snap-through. The bifurcation of second mode is studied in terms of excitation level, internal detuning and damping ratios. It is found that below the critical load parameter, the response statistics do not significantly deviate from normality. Above the critical value, where snap-through takes place, the response is strongly non-Gaussian. This research is supported by a grant from the National Science Foundation under grant number MSS-9203733 and by additional funds from the Institute for Manufacturing Research at Wayne State University.     

Characterization of the mechanical nonlinear behavior of piezoelectric ceramics

A characterization of the nonlinear behavior with high signal excitation in piezoceramic resonators was carried out. The behavior of power devices working at resonance, in which high strains are involved, is explained. A theoretical model previously described is used to explain the motional impedance variation proportional to the square of the motional current. This impedance increase DeltaZ is independent of the frequency and explains: the nonlinear elasticity that produces the A-F effect, the nonlinear mechanical losses that increase greatly close to the resonance, and the hysteresis phenomenon produced with frequency sweeps. Different methods for measuring the mechanical nonlinear coefficients of piezoceramics with high signal excitation are presented. An experimental method is proposed to measure the mechanical loss tangent and the compliance variations as a function of the mean square strain in the piezoceramic. This consists in measuring the maximum admittance and the series resonance frequency for downward frequencies. At this jumping point, the phase angle remains zero whatever the amplitude of the excitation. Two main coefficients characterizing the material mechanical nonlinearity are deduced. Experimental measurements were carried out to compare the nonlinearity of different ceramic materials in longitudinal and transverse mode.     

Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer

We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.     

Electrode-shaping for the excitation and detection of permitted arbitrary modes in arbitrary geometries in piezoelectric resonators

This paper reports theoretical analysis and experimental results on a numerical electrode shaping design technique that permits the excitation of arbitrary modes in arbitrary geometries for piezoelectric resonators, for those modes permitted to exist by the nonzero piezoelectric coefficients and electrode configuration. The technique directly determines optimal electrode shapes by assessing the local suitability of excitation and detection electrode placement on two-port resonators without the need for iterative numerical techniques. The technique is demonstrated in 61 different electrode designs in lead zirconate titanate (PZT) thin film on silicon RF micro electro-mechanical system (MEMS) plate, beam, ring, and disc resonators for out-of-plane flexural and various contour modes up to 200 MHz. The average squared effective electromechanical coupling factor for the designs was 0.54%, approximately equivalent to the theoretical maximum value of 0.53% for a fully electroded length-extensional mode beam resonator comprised of the same composite. The average improvement in S(21) for the electrode-shaped designs was 14.6 dB with a maximum improvement of 44.3 dB. Through this piezoelectric electrodeshaping technique, 95% of the designs showed a reduction in insertion loss.     

Analysis of aging of piezoelectric crystal resonators

Aging of piezoelectric (quartz crystal) resonator has been identified as one of the most important quality control problems of quartz crystal products. Aging is defined as frequency change with time. Aging in quartz resonators can be due to several sources: mass transfer due to contamination inside the resonator enclosure, stress-strain in the resonator blank, quartz defect, etc. In this study, the stress-strain effect, which has been believed as a dominant factor contributing to aging, is studied. The stress-strain effect is caused mainly by the long-term viscoelastic properties of bonding adhesive that attach quartz crystal plate to the ceramic base package. With the available accelerating testing method under elevated temperatures, the stress-strain induced aging in the quartz crystal resonators can be investigated. Because of the miniaturized size of the resonator, a digital image analysis method called image intensity matching technique (IIMT) is applied to obtain deformation patterns in the quartz blank due to thermal load. Our preliminary results showed that the unsymmetric thermal deformations may be a dominant contributing factor to aging. For simulation purposes, finite-element analysis is used to investigate the deformation patterns (i.e., stress-strain distributions) and corresponding natural frequency shift in the piezoelectric resonators. The viscoelastic behavior of mounting adhesives is incorporated into the analysis to show the dominant effect of long-term behavior of stress-strain developed in the crystal resonators. Also, some geometrical aspects-such as uneven mounting supports due to distances, volumes and heights of the adhesives-are simulated in the model.     

Electrical-field induced nonlinear conductive behavior in dense zirconia ceramic

The effect of the applied electric field on the conductive behavior of zirconia ceramics is studied by measuring its initial current-voltage curve at various temperatures. The results show that when the field strength is higher than the threshold for flash-sintering, the curves exhibit a nonlinear behavior by having an additional current on top of the linear current according to Ohm's law. Analyzing its transport behavior reveals that the additional current density is due to the extra oxygen vacancies induced by the electric field. The formation rate of the extra vacancies and associated current was related to the field strength.     

Ultrasonic study of the elastic and nonlinear acoustic properties of ceramic aluminum nitride

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of aluminum nitride (AlN) ceramic samples as functions of temperature in the range 100–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Aluminum nitride is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (C _L), shear stiffness (), adiabatic bulk modulus (B ^S), Young's modulus (E) and Poisson's ratio () are 373 GPa, 130 GPa, 200 GPa, 320 GPa and 0.234, respectively. The temperature dependences of C _L and B ^S show normal behaviour and can be approximated by the conventional model for vibrational anharmonicity. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Grüneisen parameters. The values determined at 295 K for the hydrostatic-pressure derivatives (C _L/P) _P=0, (/P) _P=0 and (B ^S/P) _P=0 are 4.7 ± 0.1, 0.22 ± 0.03 and 4.4 ± 0.15, respectively. The adiabatic bulk modulus B ^S and its hydrostatic-pressure derivative (B ^S/P) _P=0 are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (_L), shear (_S), and mean (^el) acoustic-mode Grüneisen parameters of AlN are positive: the zone-centre acoustic phonons stiffen under pressure. The shear _S (=0.006) is much smaller than the longitudinal _L (=1.09) accounting for the low thermal Gr¨neisen parameter ^th (=0.65) obtained for this ceramic: since the acoustic Debye temperature _D (=980 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic AlN.     

非线性弹性直杆纵振时的混沌行为

研究了S形本构关系的弹性直杆纵振时的混沌行为.用Galerkin原理将杆纵振时的动力控制方程转化为二阶三次非线性微分动力系统;给出了其产生同宿轨道和异宿轨道的条件,得到了同宿轨道的参数方程;借助Melnikov函数给出了系统发生混沌的临界条件;数值计算给出了混沌运动区域随β和γ的变化规律,用分岔图、位移时程曲线、相平面图和Poincaré映射判断了系统的运动行为即定常还是混沌.进一步的研究还表明本构关系中的二次非线性项对系统的动力响应具有很大的影响.     

Multilayer piezoelectric ceramic transformer with low temperature sintering

The low-fired high performance piezoelectric ceramics used for multilayer piezoelectric transformer were investigated. Based on the transient liquid phase sintering mechanism, by doping suitable eutectic additives and optimizing processing, the sintering temperature of the quaternary system piezoelectric ceramics with high piezoelectric properties could be lower to about 960–1000°C. The low-temperature sintering multilayer piezoelectric transformer (MPT) has been developed. Some characteristics of MPT were systemically studied. The measurements include the frequency response of input impedance, frequency response of phase difference between input voltage and current, frequency shifting with load, input impedance changing with load, phase difference between input voltage and current shifting with load, and phase difference between input voltage and vibration velocity. The vibration modes and resonance characters of MPT were measured by a Laser Doppler Scanning Vibrometer. Several kinds of MPT with high voltage step-up ratio, high power density, high transfer efficiency and low cost have been industrially produced and commercialized. It reveals a broad application prospect for back-light power of liquid crystal display and piezo-ionizer etc.     

Experimental and numerical results of dynamics behavior of a nonlinear piezoelectric beam

This article presents a numerical formulation and experimental implementation for the dynamics behavior verification of the nonlinear piezoelectric beam through harmonic excitation. The nonlinear piezoelectric beam dynamic analysis program is developed with MATLAB software. To verify the nonlinear piezoelectric beam dynamic analysis results, the experimental results are used for the vibration analysis of a piezoelectric beam to the harmonic excitation of the base of the beam. Then, the piezoelectric effect on the output voltage, velocity, acceleration values, and the time response are obtained. Afterwards, the effects of the excitation velocity and the position of concentrated mass on the output voltage are verified.     

On the dynamic behavior of piezoelectric sensors and actuators embedded in elastic media

Summary Embedded piezoelectric sensors can be used to monitor the mechanical behaviour of structures for damage detection. This paper provides an analytical study of the dynamic behaviour of piezoelectric sensors embedded in elastic media under high frequency electromechanical loads induced by piezoelectric actuators. A generalized sensor/actuator model taking account of the deformation in both transverse and longitudinal directions of the piezoelectric sensor/actuator is developed. The dynamic load transfer between the sensors/actuators and the host medium is studied using Fourier transform method and solving the resulting integral equations in terms of the interfacial normal and shear stresses. Detailed numerical simulation is conducted to study the relation between the deformation of the sensor and that of the host medium under different loading conditions. The results show the significant effect of the geometry, the material combination and the loading frequency upon the behaviour of the sensor.     

Accurate determination of complex materials coefficients of piezoelectric resonators

This paper presents a method of accurately determining the complex piezoelectric and elastic coefficients of piezoelectric ceramic resonators from the measurement of the normalized electric admittance, Y~, which is electric admittance Y of piezoelectric resonator normalized by the angular frequency /spl omega/. The coefficients are derived from the measurements near three special frequency points that correspond to the maximum and the minimum normalized susceptance (B~) and the maximum normalized conductance (G~). The complex elastic coefficient is determined from the frequencies at these points, and the real and imaginary parts of the piezoelectric coefficient are related to the derivative of the susceptance with respect to the frequency and the asymmetry of the conductance, respectively, near the maximum conductance point. The measurements for some lead zirconate titanate (PZT) based ceramics are used as examples to demonstrate the calculation and experimental procedures and the comparisons with the standard methods.     

Control of thermally induced elastic displacement of an isotropic structural plate bonded to a piezoelectric ceramic plate

Summary The present paper deals with a thermoelastic problem in an isotropic structural plate to which a piezoelectric ceramic plate of crystal class 6mm is perfectly bonded. It is assumed that the combined plate is subjected to a thermal load and then is deformed. In this case, we try to control the deformation of the isotropic structural plate by applying an electric potential to the piezoelectric ceramic plate. By analyzing the piezothermoelastic problem in the combined plate, we obtain an appropriate applied electric potential which alters the isotropic structural plate to a prescribed deformation. Finally numerical calculations are carried out for an isotropic steel plate to which a cadmium selenide plate is perfectly bonded, and the results are illustrated graphically.