Shear resonance mode decoupling to determine the characteristic matrix of piezoceramics for 3-D modeling

The determination of the characteristic frequencies of an electromechanical resonance does not provide enough data to obtain the material properties of piezoceramics, including all losses, from complex impedance measurements. Values of impedance around resonance and antiresonance frequencies are also required to calculate the material losses. Uncoupled resonances are needed for this purpose. The shear plates used for the material characterization present unavoidable mode coupling of the shear mode and other modes of the plate. A study of the evolution of the complex material coefficients as the coupling of modes evolves with the change in the aspect ratio (lateral dimension/thickness) of the plate is presented here. These are obtained using software. A soft commercial PZT ceramic was used in this study and several shear plates amenable to material characterization were obtained in the range of aspect ratios below 15. The validity of the material properties for 3-D modeling of piezoceramics is assessed by means of finite element analysis, which shows that uncoupled resonances are virtually pure thickness-driven shear modes.     

Theoretical and experimental investigations of lateral modes in 1-3piezocomposites

Materials with a periodic microstructure show resonances caused by the elastic wave Bragg diffraction. This paper presents a simple approach to describe these resonances (called lateral resonances) in 1-3 piezoelectric composite materials which have a 2-D periodicity. Our model is based on the analysis of the propagation of transverse waves in a 2-D periodic medium of infinite thickness and takes into account the periodic and interfacial boundary conditions. This model predicts the displacement field vectors and frequencies of lateral resonances from which the phase velocity of lateral waves is determined. The theoretical and experimental variations of this velocity versus the ceramic rod width to pitch ratio are compared. It is shown that the first lateral mode frequency is maximum when the ceramic volume fraction is around 0.65. Theoretical predictions of the mechanical displacement at the composite surface are compared with measurements obtained by an interferometric laser technique. A good agreement is observed, showing that lateral waves are mainly vertically polarized     

High-frequency vibrations of piezoelectric plates driven by lateral electric fields

We study coupled face-shear and thickness-twist motions of piezoelectric plates of monoclinic crystals driven by lateral electric fields. The first-order theory of piezoelectric plates is used. Pure thickness modes and propagating waves in unbounded plates as well as vibrations of finite plates are studied. Both free vibrations and electrically forced vibrations are considered. Basic vibration characteristics including resonant frequencies, dispersion relations, frequency spectra and motional capacitance are obtained. Numerical results are presented for AT-cut quartz plates. The results are expected to be useful for the understanding and design of resonant piezoelectric devices using lateral field excitation.     

Theoretical analysis of a ceramic plate thickness-shear mode piezoelectric transformer

We perform a theoretical analysis on a ceramic plate piezoelectric transformer operating with thickness-shear modes. Mindlin's first-order theory of piezoelectric plates is employed, and a forced vibration solution is obtained. Transforming ratio, resonant frequencies, and vibration mode shapes are calculated, and the effects of plate thickness and electrode dimension are examined.     

Radiation impedance and equivalent circuit for piezoelectric ultrasonic composite transducers of vibrational mode-conversion

The piezoelectric ultrasonic composite transducer, which can be used in either gas or liquid media, is studied in this paper. The composite transducer is composed of a longitudinal sandwich piezoelectric transducer, a mechanical transformer, and a metal circular plate in flexural vibration. Acoustic radiation is produced by the flexural circular plate, which is excited by the longitudinal sandwich transducer and transformer. Based on the classic flexural theory of plates, the equivalent lumped parameters for a plate in axially symmetric flexural vibration with free boundary conditions are obtained. The radiation impedance of the plate is derived and the relationship between the radiation impedance and the frequency is analyzed. The equivalent circuits for the plate in flexural vibration and the composite transducer are given. The vibrational modes and the harmonic response of the composite piezoelectric transducer are simulated by the numerical method. Based on the theoretical and numerical analysis, two composite piezoelectric ultrasonic transducers are designed and manufactured, their admittance-frequency curves are measured, and the resonance frequency is obtained. The flexural vibrational displacement distribution of the transducer is measured with a laser scanning vibrometer. It is shown that the theoretical results are in good agreement with the measured resonance frequency and the displacement distribution.     

Finite element modelling of nanostructured piezoelectric resonators (NAPIERs)

A new modification to the traditional piezoelectric thin film bulk acoustic wave resonator (FBAR) and solidly mounted acoustic wave resonator (SMR) is proven to significantly improve their performances. The proposed design involves the surface micro/nano structuring of planar piezoelectric thin films to realize an array of a large number of rod-like structures. In contrast to the plate-like thickness extensional resonance in traditional FBAR and SMR devices, the rod-like structures can be excited in their length extensional resonance, yielding a higher electromechanical coupling factor and effectively eliminating the spurious resonances from lateral modes of vibration. The designs have been investigated by two and three-dimensional finite element analyses and one-dimensional transmissionline modelling. The results show that significant increases in the electromechanical coupling factor of ca. 40% can be achieved by using the rod-like length extensional resonances as compared with the plate-like thickness extensional resonances in traditional devices. Simulations show that rod width-to-thickness aspect ratios of less than 0.5 could result in an electromechanical coupling factor (k2eff) of over 10% for a zinc oxide device, compared with approximately 7% for a conventional design.     

Multiline two-dimensional guided-mode resonant filters

A novel multiline filter using a two-dimensional guided-mode resonant (GMR) filter is proposed. The filter concept utilizes the multiple planes of diffraction produced by the two-dimensional grating. Multiple resonances are obtained by matching the guided modes in the different planes of diffraction to different wavelengths. It is shown that the location and the separation between resonances can be specifically controlled by modifying the periodicity of the grating and the other physical dimensions of the structure. This is in contrast to the one-dimensional GMR filters where the location of the resonances is material dependent. Two-line reflection filter designs with spectral linewidths less than 1 nm and a controllable spectral separation of up to 23% of the short resonance wavelength are presented using rectangular-grid grating GMR structures. Three-line filters are designed in hexagonal-grid grating GMR structures with two independently controllable resonance locations.     

Performance improvement of rectangular-plate linear ultrasonic motors using dual-frequency drive

To improve the performances of a rectangular-plate linear ultrasonic motor for specific applications, a dual-frequency drive has been proposed and investigated. Through careful design of the rectangular piezoelectric ceramic plate, its first longitudinal resonant frequency coincides with its second lateral bending resonant frequency and is one-third of its higher lateral bending resonant frequency. When a square-wave voltage is used to drive the motor, its first longitudinal and second bending and the higher bending vibration modes are excited. Experimental results show that the maximum thrust force and maximum velocity of the motor are over 170% of those obtained from the single-frequency sine-wave drive when the voltage performance of the motor becomes saturated.     

Design analysis of miniature quartz resonator using two-dimensional finite element model

This study focused on 2-D miniature quartz plates. By assigning appropriate boundary condition using finite element modeling (FEM), the vibration of a quartz plate was analyzed for converse piezoelectric effect. The quality and stability of the resonance of a quartz plate was determined by examining changes on the response curve of resonant frequency when the length of plate was decreased or increased. A graphical user interface (GUI) was adopted to assist the finite element software to calculate the frequency responses with different length of a large number of quartz plates, and to conclude a detailed curve of resonant frequency versus size. With this diagram, changes of the resonant mode for quartz plates caused by length variation can be easily observed. An optimum size of the quartz plate is obtained from the curve. Moreover, analyses were also conducted on the electrode coverage of a quartz plate and the mass-loading effect of metallic electrodes for this study, to discuss the influence on the resonant frequencies of quartz plates.     

Magnetoelectric performance of cylindrical Ni–lead zirconate titanate–Ni laminated composite synthesized by electroless deposition

The cylindrical Ni–lead zirconate titanate (PZT)–Ni laminated composites with various magnetostrictive–piezoelectric phase thickness ratios were synthesized by electroless deposition. The influences of the bias magnetic field (H _dc) and the ac magnetic field frequency (f) on magnetoelectric (ME) effect are discussed. It is seen that the ME voltage coefficient depends strongly on H _dc and f. The ME voltage coefficient and electromechanical resonance frequency increase as the magnetostrictive–piezoelectric phase thickness ratio increases. The calculated resonant frequency increases with the magnetostrictive–piezoelectric phase thickness ratio, which agrees well with the experimental results. The maximum ME voltage coefficient of the cylindrical Ni–PZT–Ni laminated composite is 3.256 V cm⁻¹ Oe⁻¹, which is much higher than that of the plate laminated composite with the same magnetostrictive–piezoelectric phase thickness ratio. Electroless deposition is an efficient method to prepare ME laminated composites with complex structures. Proper resonant frequency and stronger ME effect can be obtained by optimizing the structure.     

Experimental measurements and finite element analysis of the coupled vibrational characteristics of piezoelectric shells

Piezoelectric plates can provide low-frequency transverse vibrational displacements and high-frequency planar vibrational displacements, which are usually uncoupled. However, piezoelectric shells can induce three-dimensional coupled vibrational displacements over a large frequency range. In this study, three-dimensional coupled vibrational characteristics of piezoelectric shells with free boundary conditions are investigated using three different experimental methods and finite element numerical modeling. For the experimental measurements, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is used to obtain resonant frequencies and radial, lateral, and angular mode shapes. This optical technique utilizes a real-time, full-field, non-contact optical system that measures both the natural frequency and corresponding vibration mode shape simultaneously. The second experimental technique used, laser Doppler vibrometry (LDV), is a pointwise displacement measurement method that determines the resonant frequencies of the piezoelectric shell. An impedance analyzer is also used to determine the resonant frequencies of the piezoelectric shell. The experimental results of the resonant frequencies and mode shapes for the piezoelectric shell are verified with a numerical finite element model. Excellent agreement between the experimental and numerical results is found for the three-dimensional coupled vibrational characteristics of the piezoelectric shell. It is noted in this study that there is no coupled phenomenon at low frequencies over which radial modes dominate. However, three-dimensional coupled vibrational modes do occur at high resonant frequencies over which lateral or angular modes dominate.     

Evaluation of piezocomposites for ultrasonic transducerapplications influence of the unit cell dimensions and the properties ofconstituents on the performance of 2-2 piezocomposites

A theoretical model on piezoceramic polymer composites with laminar periodic structure is presented. A salient feature of this model is that it can treat explicitly how the unit cell dimensions and other material properties influence the performance of an ultrasonic transducer made of 2-2 piezocomposites. The model predicts that there exist a series of modes associated with the periodic structure of a composite, which is beyond the stop-band edge resonance prediction. One of the main concerns in designing a composite transducer is how the surface vibration profile changes with frequency and how this is influenced by the aspect ratio of the ceramic plate. It was predicted that as long as the thickness resonance is below the first lateral mode frequency, there is always a frequency f₁ which is near the thickness resonance and at which the polymer and ceramic vibrate in unison. The effect of aspect ratio is to change the position of f₁ with respect to the thickness resonance frequency and the bandwidth in which polymer and ceramic have nearly the same vibration amplitude and phase. It is also predicted that, when operated in a fluid medium such as water, there will be a resonance mode which has a frequency determined by the velocity of the fluid medium and the unit cell length d and is associated with the oscillation of the fluid. The behavior of a composite plate as an acoustic transmitter and receiver and the influence of the aspect ratio of the ceramic plate on them are also investigated     

Comparison of the frequency and physical nature of the lowest order parasitic mode in single crystal and ceramic 2-2 and 1-3 piezoelectric composite transducers

This work describes an investigation into the first order parasitic mode (i.e., that closest to the fundamental thickness mode) that can occur in 2-2 and 1-3 thickness drive piezoelectric composite transducers. Specifically, the authors compare the performance of piezoceramic and piezocrystal composites with a common passive phase. A local Lamb wave approach is used to describe the generation of such modes, and the validity of this theory is investigated over the entire volume fraction range. It is shown that, when the parasitic mode is primarily generated by Lamb wave activity in the passive phase, both active materials demonstrate similar behavior. However, at higher volume fractions, the first order mode is related to the lateral resonance of the active material, and quite different behavior may be observed between the two sets of devices. The phase velocity of the parasitic modes in each device configuration was investigated by a combination of experimental measurement on a number of transducers along with simulations using the finite-element code PZFlex. Both 2-2 and 1-3 composites made from the single crystal materials pzn-4.5%pt, pzn-8%pt, and pmn-30%pt were investigated along with composites made from pzt5h ceramic. The PZFlex results are compared with experimental impedance analysis and laser scanning of surface displacement, with good agreement demonstrated. By comparing two very different active materials, additional insight into parasitic resonant activity within composite devices is demonstrated.     

Characterization of electromechanical coupling coefficients of piezoelectric films using composite resonators

By analyzing the resonance frequency spectrum of a composite resonator consisting of a piezoelectric ceramic film deposited on a substrate plate, the thickness extensional mode electromechanical coupling coefficient of the film, k(t)(2), can be directly calculated from the effective coupling factor values, k(eff )(2), for two special modes of the resonator. The effects of the mechanical loss in the piezoelectric films on the measurement are investigated by numerical simulation, and some guidelines for improving the accuracy of the k(t)(2) measurement are reported.     

Researching on resonance characteristics influenced by the structure parameters of 1-3-2 piezocomposites plate

The 1-3-2 composite is made of 1-3 composite and ceramic base. Its effective properties are calculated based on the linear piezoelectric theory and uniform field theory. The influence of piezoelectric phase volume fraction and composite aspect (thickness/width) on resonance characteristic of square 1-3-2 piezoelectric composite plate has been researched. In addition, some 1-3-2 composite samples were fabricated by dice-fill technology. The resonance frequency of samples was investigated. The results show that the experiment agrees well with the calculation. The pure thickness resonance mode of 1-3-2 composite will be gained when the volume fraction of ceramic bottom is less than 30%; that of ceramic rods is in the range of 30 approximately 80% and the ratio of thickness to width is less than 0.35.     

Numerical algorithms and results for SC-cut quartz plates vibrating at the third harmonic overtone of thickness shear

Finite element matrix equations, derived from two-dimensional piezoelectric high frequency plate theory are solved to study the vibrational behavior of the third overtone of thickness shear in square and circular SC-cut quartz resonators. The mass-loading and electric effects of electrodes are included. A perturbation method which reduces the memory requirements and computational time significantly is employed to calculate the piezoelectric resonant frequencies. A new storage scheme is introduced which reduces memory requirements for mass matrix by about 90% over that of the envelope storage scheme. Substructure techniques are used in eigenvalue calculation to save storage. Resonant frequency and the mode shapes of the harmonic third overtone thickness shear vibrations for square and circular plates are calculated. A predominant third overtone thickness shear displacement, coupled with the third overtone of thickness stretch and thickness twist, is observed. Weak coupling between the third order thickness shear displacement and the zeroth-, first-, and second-order displacements is noted. The magnitudes of the lower order displacements are found to be about two orders smaller than that of the third overtone thickness shear displacement.     

Semiclassical theory to optical resonant modes of a transparent dielectric spheroidal cavity

We study the resonant scattering of light by a transparent dielectric spheroid. We try to understand the features of the resonant modes of a spheroidal optical cavity. In this way, we use an analogy between optics and quantum mechanics. Through this analogy it is possible to interpret resonances as quasibound states of light. Using semiclassical methods such as the WKB method and a uniform asymptotic expansion for spheroidal radial functions, we developed algorithms that permit us to calculate the resonance position as well as the resonance width.     

Electrically driven flexural resonant modes in symmetrically electroded X-cut and Z-cut quartz discs

While it is well known that flexural mechanical resonant modes can be electrically driven in specimens of quartz and other piezoelectric materials by the judicious choice of electrode patterns, specific experimental data, based on simultaneous interferometric observations of opposite surface points, are presented to show that symmetrically electroded X-cut and Z-cut quartz discs exhibit flexural resonant modes of quite large amplitudes. These resonances are not accompanied by detectable electrical disturbances in the AC-drive circuits. The existence of these modes is demonstrated for an X-cut quartz disc, and specific resonant modes of a Z-cut quartz disc are characterized in detail.     

一种基于Layerwise理论的压电复合材料层合圆柱壳机电耦合有限单元

基于Reddy的Layerwise理论,对含压电铺层的复合材料层合壳的静力响应特性进行了理论研究。基于Layerwise理论,推导了含压电层的复合材料层合壳的应变分量与电场强度表达式。利用Hamilton原理和变分法,推导了压电智能层合壳的欧拉-拉格朗日方程,并采用有限元解法,建立了相应的有限元控制方程及其机电耦合刚度矩阵。通过算例结果与文献中的精确解和试验值进行了对比,表明相较于传统的经典层合板壳理论,本文理论方法的有效性和优势性;并分析了径厚比等参量对两端简支压电智能层合壳静力响应值的影响规律。      

Analysis of a monolithic, two-dimensional array of quartz crystal microbalances loaded by mass layers with nonuniform thickness

We study free thickness-shear vibrations of a monolithic, two-dimensional, and periodic array of quartz crystal microbalances loaded by mass layers with gradually varying thickness. A theoretical analysis is performed using Mindlin's two-dimensional plate equation. It is shown that the problem is mathematically governed by Mathieu's equation with a spatially varying coefficient. A periodic solution for resonant frequencies and modes is obtained and used to examine the effects of the mass layers. Results show that the vibration may be trapped or untrapped under the mass layers. The trapped modes decay differently in the two in-plane directions of the plate. The mode shapes and the decay rate of the trapped modes are sensitive to the mass layer thickness.