Multilayer Piezoelectric Transducers Research Articles

Parallel differential evolution paradigm for multilayer electromechanical device optimization

Design optimization of multilayer piezoelectric transducers is intended for efficient and practical usage of wideband transducers for fault diagnosis, biomedical, and underwater applications through adjusting layer thicknesses and volume fraction of piezoelectric material in each layer. In this context, we propose a parallel differential evolution (PDE) algorithm to mitigate the complexities of multivariate optimization as well as the computation time to achieve an optimized wideband transducer for the particular application. For lead magnesium niobate-lead titanate (PMN PT)- and PZT5h-based piezoelectric materials, the fitness function is formulated based on uniformity of mechanical pressure at the first three harmonics to achieve wide bandwidth in the required functional frequency range. It is carried out using a one-dimensional model (ODM), while input layer thicknesses and volume fractions of active material are evaluated using PDE. The simulation is performed on a parallel computing platform utilizing three different host machines to reduce computational time. Results of the proposed methodology for PDE are statistically represented in the form of minimum, maximum, mean, and standard deviation of fitness value, while graphically represented in terms of speedup and time. It can be observed that the execution time for parallel DE decreases with the increasing number of cores.

Layered piezoelectric structures with arbitrary acoustic termination impedances.

Multilayer piezoelectric transducers and resonators are widely used for generating propagating and standing acoustic waves as well as for sensor devices. More recently, layered piezoelectric structures based on thin film technology became increasingly important for electromechanical filters used in mobile phones. As a consequence, analytical mathematical modeling of such structures is of high interest. In this paper, a general rigorous transfer matrix description for one-dimensional (1D) layered structures consisting of piezoelectric, visco-elastic, and dielectric layers of arbitrary number is introduced to characterize the electrical and mechanical behavior of a general piezoelectric transducer or resonator with two electrodes and arbitrary acoustic termination impedances (Rig-1D-model). This model is the most general 1D analytical description of layered piezoelectric structures available and can be used for the characterization of various composite transducer and resonant sensor applications. Considered in detail are layered structures with the technically important cases of only one electromechanically coupled mode, and the structure at one or both outer surfaces is in contact with semi-infinite media. For such devices, it is shown how the frequency dependence of the total electrical admittance and spatial dependence of the displacements can be calculated.

Printed Multilayer Piezoelectric Transducers on Paper for Haptic Feedback and Dual Touch-Sound Sensation.

With a growing number of electronic devices surrounding our daily life, it becomes increasingly important to create solutions for clear and simple communication and interaction at the human machine interface (HMI). Haptic feedback solutions play an important role as they give a clear direct link and response to the user. This work demonstrates multifunctional haptic feedback devices based on fully printed piezoelectric transducers realized with functional polymers on thin paper substrate. The devices are flexible; lightweight and show very high out-of-plane deflection of 213 µm at a moderate driving voltage of 50 Vrms (root mean square) achieved by an innovative multilayer design with up to five individually controllable active layers. The device creates a very clear haptic sensation to the human skin with a blocking force of 0.6 N at the resonance frequency of 320 Hz, which is located in the most sensitive range of the human fingertip. Additionally the transducer generates audible information above two kilohertz with a remarkable high sound pressure level. Thus the paper-based approach can be used for interactive displays in combination with touch sensation; sound and color prints. The work gives insights into the manufacturing process; the electrical characteristics; and an in-depth analysis of the 3D deflection of the device under variable conditions

Experimental validation of axially polarized multilayer piezoelectric composite cylindrical transducers with adjustable multifrequency

The axially polarized multilayer piezoelectric composite cylindrical transducers with adjustable multifrequency capability have been proposed by adjusting the external electric resistance and the ratio of piezoelectric layer numbers between the actuator part and the sensor part, which have promising potential in designing the novel cymbal transducer for underwater sound projector and ultrasonic radiator applications. In the previous studies, the multilayer models were established to guide the design of the transducers with arbitrary layer number, and analyzed the dynamic characteristics theoretically. In this work, an experimental study is performed to validate the theoretical models and predictions. Piezoelectric rings with multiple concentric annular electrodes are designed to characterize the multilayer piezoelectric composite cylindrical transducers. The top surface of the piezoelectric rings is divided into two separate parts. One part is covered by multiple concentric annular electrodes, corresponding to the piezoelectric layers, and the other part is uncovered, corresponding to the elastic layers. Four prototypes are fabricated and each consists of four concentric annular electrodes. The impedance spectra are measured by the impedance analyzer to obtain the resonance and anti-resonance frequencies. Effects of two adjusting methods on the dynamic characteristics are evaluated experimentally. The experimental results basically coincide with the theoretical ones. This comprehensive experimental work assures the feasibility of using axially polarized multilayer piezoelectric composite cylindrical transducers with adjustable multifrequencies and confirms the benefit of the developed theoretical models for guiding the fabrication and optimization of this type of transducers.

Low temperature sintering of Li2CO3 added Pb(Ni1/3Nb2/3)-Pb(Zr,Ti)O3 ceramics with high piezoelectric properties

Multilayer structure is an effective approach for reducing driving voltages or increasing output electric signal for piezoelectric devices. However, it is a challenge to achieve high piezoelectric coefficient at low sintering temperature. In this work, we fabricated Li2CO3 (LC) doped Pb(Ni1/3Nb2/3)-Pb(Zr,Ti)O3 (PNN-PZT) ceramics via solid state reaction method. Piezoelectric coefficient at low quasi-static signal d33 and effective piezoelectric coefficient under high electric field d33* are 692 pC/N, 1114 pm/V for PNN-PZT+0.2 wt% LC sintered at 950 °C, which is comparable to high temperature sintered commercial Pb(Zr,Ti)O3 (PZT) based ceramics. Detailed piezoelectric, ferroelectric, dielectric properties, temperature stability and material structure were investigated. The planar electromechanical coupling factor Kp, relative dielectric constant εr and dielectric loss tan δ at 1 kHz, Curie temperature Tc, coercive electric field Ec are measured to be 0.557, 4280, 0.025, 113 °C, 4.34 kV/cm. It shows great potential for applications in multilayer structured cofired piezoelectric actuators and transducers.

Weighted differential evolution heuristics for improved multilayer piezoelectric transducer design

Piezoelectric transducers are designed for wide applications of underwater sonar, energy harvesting, biomedical and nondestructive testing in terms of higher sensitivity and broad bandwidth. Multilayer transducers have well-known advantages of higher sensitivity and thus can be optimized by varying layer thicknesses of active material. The present study deals with mathematical optimization of multilayer transducers exploiting weighted differential evolution (WDE) based computational heuristics for optimized piezoelectric transducer design while satisfying the constraint of constant total thickness. Fitness evaluation is carried out on the basis of one dimensional model (ODM) for simple multilayer, multilayer with bondlines and transducer with bondlines and matching for piezoelectric materials including PZT5h, PMN-PT and piezocomposite with PMN-PT for different loading media. WDE exploited along with ODM for the transducer models has demonstrated the efficacy, reliability and applicability of the proposed scheme. Comparative study of the proposed WDE-ODM with its counterparts including simulated annealing, genetic algorithms, and particle swarm optimization, reveal better performance in terms of accuracy, complexity and convergence metrics for different number of layers for simple transducers. Applicability of WDE-ODM on piezoelectric structures with bondlines, and matching layers has also been accessed and validated.

Soft Acoustic Waveguides for Strain, Deformation, Localization, and Twist Measurements

A novel type of soft tactile sensor based on polymeric acoustic waveguides is proposed. Ceramic multi-layer piezoelectric transducers generate ultrasonic acoustic wave packets (980kHz) that propagate and can be attenuated, delayed and reflected based on waveguide deformation and length. We detail the sensor design, manufacture and operation and then propose 6 experiments in which we measure the sensor performance. The sensor can detect strain (up to 80%), normal deformation (up to 1mm), simultaneous strain and deformation, compression location (0.5mm interval) and twists (up to 400 axial rotations per meter) and is insensitive to bending (up to 250m−1). This work is the first to propose using soft polymeric waveguides as a tactile element for strain, deformation, localization and twist measurement. This is also the first work to demonstrate decoupled strain and deformation sensing in a single, soft, sensing element. This research aims at introducing an innovative sensing method that can be leveraged toward the creation of simpler and denser multi-modal soft sensors.

Energy harvester for safety shoes using parallel piezoelectric links

Energy-harvesting devices in shoes have attracted much attention from the fields of elderly support, sports science, and disaster mitigation. In this study, we developed an energy harvester with a parallel link structure and six multi-layered piezoelectric transducers. By using this structure, we realized an effective energy conversion compared with conventional energy harvesters in terms of maximum power, comfort, durability, and availability of inputs with six degrees of freedom. A prototype of the parallel-link piezoelectric energy harvester generated 1.29 mW with human body weight. As a trial use, this energy harvester was installed in safety shoes for powering LEDs in the shoes. The assembly produced a brightness of 0.5 cd on average over a duration of 0.5 s, which is enough to show the wearer his or her position in a dark place.

Effects of electrodes and electrical connections of piezoelectric layers on dynamic characteristics of radially polarized multilayer piezoelectric cylindrical transducers

Piezoelectric cylindrical transducer is a type of excellent smart devices that can generate radial sound radiation due to its unique structural characteristics and has been widely used for ultrasonic and underwater sound applications. In the design of a piezoelectric cylindrical transducer, especially with the multilayer structure, the electrodes and electrical connections of piezoelectric layers are two key factors affecting the device performance but have not been well evaluated, which result in the inaccurate prediction of dynamic characteristics. This work establishes the exact theoretical models for radially polarized multilayer piezoelectric cylindrical transducers by taking into account the electrodes and electrical connections of piezoelectric layers. Based on the plane stress assumption, the dynamic solutions of the models are derived. Analytical expressions of electric impedances are also derived to obtain the resonance frequencies. In addition, the analytical solutions are validated using the special example in the earlier work and comparing them with the finite element analysis results. Subsequently, the effects of the electrodes and electrical connections of piezoelectric layers on the dynamic characteristics of the transducer are analyzed and discussed. The results show that the electrode thickness, the electrode type, and the parallel and series connections significantly affect the transducer’s performance, thus providing useful guidelines in the design of piezoelectric cylindrical transducers. This work contributes to an overall analysis on the dynamic characteristics of the radially polarized multilayer piezoelectric cylindrical transducers, which is very helpful to improve the performance of two-dimensional emitter and receiver in underwater sound and ultrasonic applications.

New trends in fundamental research due to the spontaneous flexoelectric effect in nanosized and bulk ferroelectrics

Physical processes taking place at the surface and its vicinity are so rich and versatile that sometimes seems to be inexhaustible subject of fundamental researches, which open new ways of technical applications. In particular theoretical and experimental researches of the versatile flexoelectric phenomena at nanoscale remain hot topic during last 10 years. Among them the special attention attracts the spontaneous flexoelectric effect inherent to nanosized and nanostructured ferroelectrics, as originated from the intrinsic polarization inhomogeneity near the surface of the system. The effect revealed in 2009 is very important, since it leads to the strong increase of effective flexoelectric coefficients values due to size effect. So that at small sizes the spontaneous flexoeffect strongly influences polar, piezoelectric and dielectric properties as well as the correlation radius. Motivated by above argumentation the author review describes the way of nanoscale ferroelectric properties and phase diagram calculations in the framework of Landau-Ginzburg-Devonshire thermodynamic theory with special attention to flexoelectric effect contribution. The comparison of obtained results with available experimental data is given whenever possible.The review highlights recent calculations, which have shown that the spontaneous flexoelectric effect and chemical pressure can be the physical reason of ferroelectric phase conservation and reentrance observed in spherical ferroelectric nanoparticles up to 5 nm sizes. Fundamental results devoted to the finding of “forbidden” shear surface wave propagating near the surface of all ferroelectrics due to omnipresent flexoelectric coupling are discussed. These missed surface waves are waiting for experimental observation, which could be the source of unique information about surface impact on the dynamics, structural peculiarities and possible phase transitions induced by the surface. Also we analyze how significantly the flexoelectric coupling can change static and dynamic polar properties in ferroelectrics, govern the formation and growth of unusual domains structures and influence optic and acoustic soft modes. The special attention in the review in paid to recent results, which have shown that flexocoupling induces soft acoustic mode in response of spatially modulated phase appearance in flexoelectrics.We'd like to underline that theoretical and experimental studies of flexoelectricity and related phenomena in nanosized and bulk ferroelectrics are very important for applications in nanoelectronics and memory devices, opening the way of true minimization of multilayer ceramic capacitors, piezoelectric transducers, pyroelectric elements and ferroelectric memories.

A distributed parameter model for the piezoelectric stack harvester subjected to general periodic and random excitations

Vibration-based energy harvesting using piezoelectric stacks has received increasing attention in recent years for its higher mechanical-to-electrical energy conversion capability in the d33 mode. However, most research on this type of harvesters is based on either the simplified one-degree-of-freedom model or transfer matrix model. This paper presents a distributed-parameter model for the multilayer piezoelectric stack transducer based on the axial vibration theory of a continuous bar. The presented analytical model is free from the assumption that the generated current is identically distributed over all the piezoelectric layers, which has been widely used by the existing models in literature. A first-order numerical model is also introduced to validate the performance of the analytical model on the prediction of voltage, current and power outputs of the harvester under different types of external excitations. Both the analytical and numerical models are firstly validated by experiments and then are used to predict the electrical responses of the stack harvester under general periodic and random excitations with different intensities. Experiment and simulation results demonstrate that the proposed distributed-parameter model has a good accuracy and reliable performance in the prediction of the electrical responses.

Modeling a multilayer piezo-electric transducer by equivalent electro-mechanical admittance matrix

Piezoelectric transducers (sensors and actuators) are widely used to produce motion or to sense displacement. One of the most applicable types of the piezo-electric transducers is a transducer in which the piezo stacks are sandwiched between two vibrating masses by a connecting stud. These types of the piezo-electric transducers which are utilized for sensing applications are known as Tonpilz. A piezo-electric transducer is usually designed to work in the resonant frequency, and modeling and simulating its dynamics behavior to check the desired performance are very important. In this study, by considering the concept of the admittance expression, the dynamics model of a piezo-electric transducer is derived, and based on it, the characteristics of the longitudinal vibration of the piezo-electric transducer are calculated. The admittance expression is in the matrix notation which contains the equivalent admittance matrices correspond to the various composing parts of the transducer. The matrix notation provides a flexible and simple way for modeling the piezo-electric transducer, by combining the various containing parts of the piezo-electric transducers. To calculate the equivalent admittance matrix, at first, the equivalent admittance matrices of the metallic and piezo-electric parts of the transducer are derived, and then they are collected in one matrix diagonally. Then, by applying the boundary conditions via matrix operations, the equivalent admittance matrix of the transducer is obtained. One of the benefits of this modeling is obtaining the optimal design by considering different parameters. At last, the obtained analytic model is verified by experimental measurements of some fabricated transducers, which shows a good agreement.

Bio-inspired heuristics for layer thickness optimization in multilayer piezoelectric transducer for broadband structures

Recently, enhancement of sensitivity of multilayered piezoelectric transducer and reduction in electrical impedance has gained importance due to development of stacked active element designs. This work presents mathematical optimization of layer thicknesses for broadband structures using piezo-composite with ceramic and single crystal as active material for underwater SONAR. The proposed technique employs bio-inspired heuristics-based genetic algorithms by invoking one-dimensional thickness model. Initially, optimization has been performed for monolithic materials in the stack for various acoustic media, and then, the results were validated by comparing with the published data. In the proposed scheme, optimization is carried out for two-phase 1–3 piezo-composite stacks with same active elements for better mechanical output and broadband structure while preserving the minima among first three harmonics under $$-\,3$$ and $$-\,6$$ dB from the peaks in the frequency spectrum. The results show that the optimized single-crystal-based transducers have higher mechanical output and lower electrical impedance than their counterparts using piezo-ceramic in single- and two-phase materials.

가진부와 감지부를 구분한 다층 압전 트랜스듀서의 진동 특성

This paper deals with the vibration characteristics of a multilayered piezoelectric transducer. The transducer consists of multiple piezoelectric layers for exciting, one piezoelectric layer for sensing and insulation layers. Theoretically, natural frequencies and mode shapes of radial in-plane modes of the piezoelectric transducer were obtained from equations of motion and boundary conditions. By the finite element modal analysis, the natural frequencies were obtained from calculated impedance curves, and the vibration amplitudes were calculated to supplement three-dimensional mode shapes. Experimentally, the natural frequencies were measured by an impedance analyzer. The theoretical analysis was verified by comparing three kinds of results, and it was confirmed that the vibration exciter and sensor of a transducer could be separated by piezoelectric multilayers.

Parametric block diagrams of a multi-layer piezoelectric transducer of nano- and microdisplacements under transverse piezoelectric effect

A structural-parametric model and parametric block diagrams of a piezoelectric transducer in the transverse piezoelectric effect are obtained with regard to the counter-electromotive force. The transfer functions of the multi-layer piezoelectric transducer of nano- and microdisplacements are determined with regard to the influence of geometric and physical parameters of the multi-layer piezoelectric transducer, the counter-electromotive force, and the external load.

Reconciling Local Structure Disorder and the Relaxor State in (Bi1/2Na1/2)TiO3-BaTiO3.

Lead-based relaxor ferroelectrics are key functional materials indispensable for the production of multilayer ceramic capacitors and piezoelectric transducers. Currently there are strong efforts to develop novel environmentally benign lead-free relaxor materials. The structural origins of the relaxor state and the role of composition modifications in these lead-free materials are still not well understood. In the present contribution, the solid-solution (100-x)(Bi1/2Na1/2)TiO3-xBaTiO3 (BNT-xBT), a prototypic lead-free relaxor is studied by the combination of solid-state nuclear magnetic resonance (NMR) spectroscopy, dielectric measurements and ab-initio density functional theory (DFT). For the first time it is shown that the peculiar composition dependence of the EFG distribution width (ΔQISwidth) correlates strongly to the dispersion in dielectric permittivity, a fingerprint of the relaxor state. Significant disorder is found in the local structure of BNT-xBT, as indicated by the analysis of the electric field gradient (EFG) in 23Na 3QMAS NMR spectra. Aided by DFT calculations, this disorder is attributed to a continuous unimodal distribution of octahedral tilting. These results contrast strongly to the previously proposed coexistence of two octahedral tilt systems in BNT-xBT. Based on these results, we propose that considerable octahedral tilt disorder may be a general feature of these oxides and essential for their relaxor properties.

Theoretical and Experimental Investigation of Ultrasonic Transducers With Dual Oppositely Polarized PMN-PT Layers in Wide Frequency Range

The electrical and acoustic characteristics of a two-layered piezoelectric transducer in a broad frequency range are investigated. The theoretical modeling of the transducer having dual oppositely polarized lead magnesium–lead titanate (PMN-PT) layers based upon KLM equivalent circuit theory with the complex piezoelectric material constants is reported. The complex material constants of the piezoelectric single crystal including the frequency-dependent loss properties are obtained by fitting the measured electrical impedance resonance characteristics. The electrical impedance and surface vibration displacement characteristics at frequencies up to the third harmonic of the two-layered piezoelectric transducers with various layer thicknesses are studied by simulation and measurement. It is found that the nonuniformity of the two active layer thicknesses promotes the second harmonic of the electrical and acoustic frequency characteristics, which can be optimized to extend the bandwidth of multilayer piezoelectric transducers. The reported model with the complex piezoelectric material constants can predict the electrical impedance of the multilayer piezoelectric transducers with the agreement functions above 69% and the characteristic frequency errors below 3.03% over the frequency range covering the first three harmonics. The predicted harmonic frequency errors of the acoustic output are less than 6.8%. This work fundamentally supports the design and optimization improvement of multilayer piezoelectric ultrasonic transducers for wide frequency range applications.

Optimal design of a multilayered piezoelectric transducer based on a special unit cell homogenization method

Piezoelectric transducers with high directional-dependent response are of interest in several applications because of their ability to sense and actuate along specific directions where they can distinguish individual principal strain components. This paper presents an improved unidirectional sensor obtained using a multi-laminate piezocomposite that maximizes the electromechanical coupling factor or the piezoelectric strain constant in one direction with respect to the other directions. Furthermore, multi-laminate structures provide significant design potential by the variation of the orientation and stacking sequence of fibers to obtain the desired properties. The effective properties depend on the number of layers, the fibers orientation as well as the thickness of each layer, and they are estimated by the variational asymptotic method for unit cell homogenization. A design that guarantees maximum directional dependence in terms of piezoelectric strain constant is determined by a global optimization technique using a genetic algorithm. Layered transducers composed of several orthotropic passive layers and a single active layer are considered.

Three-port equivalent circuit of multi-layer piezoelectric stack

Multi-layer piezoelectric transducers (MPS) is a transducer stacked by numerous thin piezo layers, which can used as an actuator, sensor, or energy harvester. This paper points out the limitations of existing equivalent circuits for the effective modelling of MPS and proposes a 3-port equivalent circuit of MPS which is inspired by the idea of network theory and formulated exactly on the basis of the simplified fundamentals. The 3-port equivalent circuit, which separates the MPS into two acoustic ports and one electrical port through an electro-mechanical transformer, offers an exact and explicit representation of electro-mechanical coupled interaction of MPS. It is very straightforward to apply and effectively simplifies and facilitates the analysis, modelling, and calculation of free and loaded vibration of MPS in either transmitter mode (actuator) or receiver mode (sensor or energy harvester). Compared with existing circuit models in literature, the proposed circuit can be extended to any electrical and mechanical condition. Besides, as the proposed circuit elements are explicitly and exactly derived in terms of material and dimension information rather than determined from measured information, the proposed circuit model allows one to predict behaviors with material properties and structural dimension. For validation, a simple case study is carried out. For both free and loaded vibrations of MPS in the case study, the effectiveness of the proposed circuit has been validated by 3D FEA models.

Parametric block diagrams of nano- and microdisplacement multilayer piezoelectric transducer in longitudinal piezoeffect

Parametric block diagrams are constructed for the multilayer piezoelectric transducer in longitudinal piezoeffect with the counter-electromotive force taken into account. The transfer functions of the multilayer piezoelectric transducer are obtained with regard to the influence of geometric and physical parameters of the multilayer piezoelectric transducer, counter-electromotive force, and external load.