Multilayer Transducers Research Articles

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.

Modeling and analysis of multilayer piezoelectric-elastic spherical transducers

An exact analytical model of multilayer piezoelectric-elastic spherical transducers is established in this article, and their dynamic characteristics are studied. Based on the linear theory of piezoelasticity, the dynamic analytical solution is derived in terms of Bessel functions, Lommel functions, Gamma functions, and Generalized Hypergeometric functions, and the electric impedance is obtained to determine the resonance frequencies. By proper selection of the layer number and geometric dimensions, the proposed model can approximately degrade into some special cases in the previous works, including single-layer piezoelectric spherical transducer, two-layer piezoelectric-elastic spherical transducer, and three-layer sandwiched piezoelectric-elastic-piezoelectric spherical transducer. Comparisons between the results of the proposed model and the ones of these special cases are also given and good agreements are found. Furthermore, parametric studies are conducted to discuss the effects of the key parameters on the dynamic characteristics of these special cases and a multilayer case, such as the first resonance and anti-resonance frequencies as well as the corresponding electromechanical coupling factor. This work contributes to an overall understanding of the dynamic characteristics of miniature piezoelectric hollow sphere transducers (BBs) and stacked piezoelectric spherical transducers. The developed model can be used to guide the design of the multilayer piezoelectric-elastic spherical transducers for promising applications in underwater acoustic detection, ultrasonic imaging, hydrophones, and nondestructive testing.

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.

Characterization of Au/Fe/Au and Au/Co/Au Magneto-Plasmonic Multilayers as an Ethanol Vapor Sensor

In this paper, we investigate the sensing performance of Au/Fe/Au and Au/Co/Au magneto-plasmonic nanostructures as transducers as well as the performance of TiO2 thin film and TiO2 NPs as sensing layers. A comparison between sensing performance of the traditional surface plasmon resonance (SPR) and the magneto-optic (MO) SPR (MOSPR) transducing techniques is presented here. The surface plasmon wave vector in these transducers which are consisted of metallic and magnetic materials is modulated by external magnetic field in the transverse configuration. Magneto-plasmonic structures show a great enhancement of an MO Kerr effect when the SPR condition is satisfied. As such enhancement strongly depends on the excitation conditions of the surface plasmon polariton (SPP) and, therefore, on the refractive index of the dielectric in contact with the metal layer, we use this enhanced MO signal as the sensing magnitude for investigating molecular interactions between ethanol vapor and TiO2 nanostructures onto the transducers. Besides, when the SPP is excited, applied magnetic field would modulate the SPP wave vector. The modulated nature of MOSPR signal would lead to a higher sensing performance in terms of sensitivity and signal-to-noise ratio with respect to the traditional SPR signal. Moreover, our results show that using TiO2 NPs in the vicinity of multilayer transducers creates a better sensing performance which is caused by porosity and enhancement in the surface area of absorbent layer.

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.

The co-casting process: A new manufacturing process for ceramic multilayer devices

In this work we present a simplified process chain of the conventional multilayer ceramic technology and offer a comfortable method for precise multilayer manufacturing without complex equipment. To circumvent the usual stacking and laminating of single ceramic green tapes to get multilayer devices, a Magnetically Assisted Stencil Printing (MASP) technique was developed. It enables a subsequent casting of ceramic layers and printing of electrode layers. How the co-casting process can be performed either by the use of a modified tape caster at the lab scale or by use of a precision squeegee is described in this paper. Both variants are suited for manufacturing multilayer ceramics with layer thicknesses less than 25μm. We successfully manufactured pentalayers without cracks or de-laminations from a soft- and also a hard-PZT powder. In a previous work, we investigated sintering additives for PZT. By the use of a PZT-based low-temperature sintering powder composition, cost-effective silver inner electrodes could be realized inside the multilayer ceramics. Piezoelectric low-cost multilayer bending transducers are of particular interest for the use as generators in vibration energy harvesting systems. The proposed triplelayer beam harvests 20μW (3.2V) at 71Hz and an input acceleration of 17.8m/s2.

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.

Analytical modeling and optimization of DEAP-based multilayer stack-transducers

Transducers based on dielectric electroactive polymers (DEAP) use electrostatic pressure to convert electrical into mechanical energy or vice versa. To scale up the actuation or the energy gain, multilayer transducers like DEAP stack transducers are appropriate. Within this contribution, a model of such a stack transducer is derived and experimentally validated. The model is based on a multi-domain approach to describe the mechanical dynamics and the electrical behavior of the DEAP. Since these two domains influence each other they are coupled afterwards by a novel approach using interchanging power flows. To parametrize this model, tensile and compression tests for different polymer materials were performed under static and transient considerations. The results of these experiments show that the parameters obtained from the tensile test sufficiently describe the compression mode and can therefore be used for the model. Based on this transducer model the overall energy and the different parts of the multi-domain are analytically determined for arbitrary operating points. These expressions for the energies are finally used to optimize well-defined coupling coefficients, by which a maximum part of the electrical input energy is converted to mechanical energy, especially mechanical work.

Modeling and optimization of adjustable multifrequency axially polarized multilayer composite cylindrical transducer

A novel adjustable multifrequency axially polarized multilayer composite cylindrical transducer is developed in this paper. The transducer is composed of two parts: an actuator part and a sensor part. Each part is considered as a multilayer piezoelectric/elastic composite structure. The actuator part is utilized to actuate the transducer, while the senor part is used to adjust its dynamic characteristics through connecting to an external electric resistance. Based on the plane stress assumption, the radial vibration of this new kind of transducer is analyzed, and its input electric admittance is derived analytically. Comparisons with the earlier works are conducted to validate the theoretical solution. Furthermore, numerical analysis is performed to study the effects of the external electric resistance on the transducer’s dynamic characteristics, such as resonance and anti-resonance frequencies, as well as the corresponding electromechanical coupling factor. Numerical results show that the multifrequency cylindrical transducer can be designed through adjusting the external electric resistance and the ratio of piezoelectric layer numbers between the actuator part and the sensor part. In addition, the optimized transducer can be proposed at the matching electric resistance. The proposed cylindrical transducer plays an important role in designing the cymbal transducer, which can be used in underwater sound projectors and ultrasonic radiators.

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.

Modeling of micromachined silicon–polymer 2-2 composite matching layers for 15 MHz ultrasound transducers

Silicon–polymer composites fabricated by micromachining technology offer attractive properties for use as matching layers in high frequency ultrasound transducers. Understanding of the acoustic behavior of such composites is essential for using them as one of the layers in a multilayered transducer structure. This paper presents analytical and finite element models of the acoustic properties of silicon–polymer composites in 2-2 connectivity. Analytical calculations based on partial wave solutions are applied to identify the resonance modes and estimate effective acoustic material properties. Finite Element Method (FEM) simulations were used to investigate the interaction between the composite and the surrounding load medium, either a fluid or a solid, with emphasis on the acoustic impedance of the composite. Composites with lateral periods of 20, 40 and 80μm were fabricated and used as acoustic matching layers for air-backed transducers operating at 15MHz. These composites were characterized acoustically, and the results were compared with analytical calculations. The analytical model shows that at low to medium silicon volume fraction, the first lateral resonance in the silicon–polymer 2-2 composite is defined by the composite period, and this lateral resonant frequency is at least 1.2 times higher than that of a piezo-composite with the same polymer filler. FEM simulations showed that the effective acoustic impedance of the silicon–polymer composite varies with frequency, and that it also depends on the load material, especially whether this is a fluid or a solid. The estimated longitudinal sound velocities of the 20 and 40μm period composites match the results from analytical calculations within 2.7% and 2.6%, respectively. The effective acoustic impedances of the 20 and 40μm period composites were found to be 10% and 26% lower than the values from the analytical calculations. This difference is explained by the shear stiffness in the solid, which tends to even out the surface displacements of the composites.

Low-frequency transducers that contain piezoelectric and passive layers

The problem of obtaining short echo-signal pulses using multilayer transducers that consist of alternating active and passive layers is considered. The time characteristics of a transducer for a frequency range of 50–500 kHz are analyzed. The main requirements that are imposed on the transducer, amplifier, and generator of the electronic unit are formulated. The parameters of the transducer that allows the duration of an echo pulse to be reduced to a value that is approximately 5–10 times smaller than the pulse duration, which results from the use of a single piezoelectric element, are determined.

A multilayer transducer that contains piezoelectric layers

Formulas for the transfer functions and electric resistance for transducers that consist of an arbitrary number of active (piezoelectric) and passive layers are obtained. Parallel and series electrical connections of layers are considered. Formulas for reducing any active layer to a passive one are obtained. On the basis of the analysis of the obtained expressions and presented calculation results, recommendations for the practical use of the considered transducers are expounded. The obtained data allow the development of transducers with appreciably improved characteristics in comparison to the case where only one active element is used. The proposed new calculation method makes it possible to substantially simplify the determination of formulas for an arbitrary number of layers. The formulas for the main functions of a transducer concern multiple three-sided transducers, on one side of which certain conditions for their electrical connection are imposed. The transfer functions for the reception mode with respect to the voltage at the working surface of the transducer are obtained. The proposed calculation method can be also applied to other types of transducers.

Resonant-Type Smooth Impact Drive Mechanism Actuator Operating at Lower Input Voltages

We report on the design and fabrication of a resonant-type smooth impact drive mechanism (SIDM) actuator based on a multilayered piezoelectric ceramic transducer. Conventional SIDMs use off-resonant sawtooth-shaped displacement in developing stick–slip motion of a slider, but require large input voltages for high-speed operation. In contrast, in resonant-type SIDMs, a quasi-sawtooth-shaped displacement is obtained by combining two resonant vibrational modes. This driving principle enables low input voltage operations. In combining the modes, their frequency ratio must be 1:2. To design and optimize the stator transducer to generate sawtooth-shaped displacements, a transfer matrix method was adopted. With a preload of 270 mN, the no-load speed was 40 mm/s under a driving voltage of 1.6 V (peak to peak). This input voltage was one-sixth that of previous SIDMs for the same performance. Concurrently, heat generation was significantly reduced because dielectric losses were suppressed under the lower input voltage operation.

Piezoelectric Properties of Fine-Grained Pb(Mg1/3Nb2/3)O3–Pb(Zr,Ti)O3–Bi(Zn1/2Ti1/2)O3 Quaternary Solid Solution Ceramics

On the basis of solid state reaction eutectic behavior between Pb(Mg1/3Nb2/3)O3–Pb(Zr,Ti)O3 (PMN–PZT) and metastable perovskite-type Bi(Zn1/2Ti1/2)O3 (BZT), perovskite-structured PMN–PZT–BZT quaternary solid solution piezoceramics with various compositions were experimentally demonstrated with an intrinsic low sintering temperature in the windows of 950–1050 °C. These fine-grained densified PMN–PZT–BZT ceramics were able to be poled sufficiently at room temperature through polarization–electric field hysteresis loop measurement, different from normal poling treatment with DC bias field at high temperature, which will simplify future device processing of monolithic multilayer piezoceramic transducers. A typical piezoelectric property of dielectric constant ε33T/ε0 = 3471, piezoelectric constant d33 = 480 pC/N, planar coupling coefficient kp = 0.41, thickness coupling coefficient kt = 0.50, mechanical quality factor Qm = 68 and relaxor ferroelectric phase transition temperature Tm = 167 °C at 1 MHz was obtained for the fine-grained densified Pb0.96Sr0.04(Mg1/3Nb2/3)0.37Zr0.24Ti0.39O3+3%Bi(Zn0.5Ti0.5)O3+2%NiO ceramics sintered at 1020 °C, which is much promising to manufacture monolithic multilayer piezoelectric transducers with Ag95/Pd5 as inner electrode material.

Mechanical and control characteristics of multilayer piezoelectric transducers of nano- and microdisplacements

Mechanical and control characteristics of a multilayer piezoelectric transducer of nanoand microdisplacements in the case of parallel and encoded control are obtained. The static and dynamic characteristics of simple and multilayer piezoelectric transducers of nano- and microscopic displacements are determined for longitudinal and transverse piezoeffects.