Piezoelectric Parameters Research Articles

Two-frequency parametric excitation and combination resonance of a nanocomposite laminated piezoelectric trapezoidal plate in subsonic airflow

In this study, an analytical approach is presented to analyze the bifurcations and nonlinear dynamics of a cantilevered piezoelectric nanocomposite trapezoidal actuator subjected to two-frequency parametric excitations in the presence of subsonic airflow. The assumption of uniformly distributed single-walled carbon nanotubes along the thickness is taken into the consideration. The governing equations are built by the von-Karman nonlinear strain-displacement relations to consider the geometrical nonlinearity and the linear potential flow theory. The present study focuses on a specific resonance case deals with the occurrence of simultaneous resonances in the principal parametric resonance of the first mode and combination of the parametric resonance of the difference type involving two modes. The multiple scales method is employed to obtain the four nonlinear averaged equations which are solved by using the Runge-Kutta method. Moreover, the frequency-response curves, bifurcation diagrams, time history responses, and phase portrait are obtained to find the nonlinear dynamic responses of the plate. The effects of the amplitude of piezoelectric excitation, piezoelectric detuning parameter, and aerodynamic pressure are also studied. The results indicate that, the chaotic, quasi-periodic and periodic motions of the plate exist under certain conditions and the variation of controlling parameters can change the form of motions of the nanocomposite piezoelectric trapezoidal thin plate.

Squared figures of merit and electromechanical coupling factors of a novel lead-free 1–3–0 composite for sensor and energy-harvesting applications

Piezoelectric sensitivity and energy-harvesting parameters are studied for a novel lead-free 1–3–0 composite where domain-engineered single-crystal rods are surrounded by a polymer matrix containing two types of air pores. Correlation between some effective parameters, concerned with the high piezoelectric sensitivity of the composite, and the elastic properties of its porous matrix is first stated. Diagrams are first built to show volume-fraction ranges wherein conditions for large squared figures of merit (Q33*)2=d33* g33*≥200⋅10−12 Pa−1 (longitudinal) and (Qh*)2=dh* gh*≥50⋅10−12 Pa−1 (hydrostatic) hold, where d33*, dh*. g33*, and gh* are piezoelectric coefficients of the composite. The studied composite is also of interest due to its large electromechanical coupling factors kt* ≈ 0.8–0.9 (thickness) and kh* ≈ 0.5–0.6 (hydrostatic). Piezoelectric sensitivity, electromechanical coupling factors and other characteristics are compared to those of a lead-containing 1–3–0 composite and a few 1–3 composites. Correlation between the effective parameters of the 1–3–0 composite and elastic properties of its porous matrix is discussed. Replacing the parallelepiped-shaped single-crystal rods with the cylindrical rods in the 1–3–0 composite leads to minor changes in the aforementioned parameters. The performance of the studied lead-free 1–3–0 composite proves its suitability for modern piezoelectric sensors, energy-harvesting and hydroacoustic devices.

Piezoelectric method‐based harvested energy evaluation from car suspension system: Simulation and experimental study

AbstractThe main objective of this work is to build a mathematical model to evaluate the potential of harvesting power from the car suspension system. Quarter‐ and half‐car models with built‐in piezoelectric stack were modeled mathematically and simulated using MATLAB/Simulink. The piezoelectric stack was installed in series with the suspension spring to maintain the performance of the original car suspension system in ride quality and comfortability. The harvested voltage and power were tested with respect to time and frequency. From a half car model, the maximum generated voltage and power at the excitation frequency of 1.46 Hz were 33.56 V and 56.35 mW, respectively. By comparing a half‐car model with the quarter‐car model, the outcomes illustrated that the harvested voltage and power of the half‐car model were increased by 75.6% and 53.4%, respectively. Piezoelectric stack parameters (number of stack layers and area to thickness) and the car suspension parameters (sprung and unsprung stiffness, damping coefficients, and masses) were examined for half‐car model. Also, the influence of road amplitude unevenness was considered. The simulation results of the quarter‐car system were verified with the experimental test under harmonic excitation. The results exhibited good agreement with the simulation results at different excitation frequencies.

Influence of an Electrostatic Field on Saw in Prestressed Ferroelectric Heterostructures

An approach to modeling a ferroelectric heterostructure with a prestressed coating made of a two-component functional-gradient material is proposed. Various types of PZT-based ceramics with close values of elastic moduli and significant differences in piezoelectric and dielectric parameters are considered as coating materials. The initial stress state (ISS) of the coating is caused by the action of an electric field and uniaxial mechanical tension. By the example of the problem of the propagation of sh-waves, the influence of the initial electrostatic field on the features of the SAW propagation has been investigated for various ratios of the parameters of the coating materials and the nature of the inhomogeneity localization.

The propagation of uncertainty in the geometrically nonlinear responses of smart sandwich porous cylindrical shells reinforced with graphene platelets

This paper is concerned with the analysis of uncertainty propagation in the nonlinear dynamic responses of smart sandwich cylindrical shells under rectangular, sine, and exponential loads. The sandwich shells are composed of a functionally graded porous (FGP) core reinforced with nanocomposite graphene platelets (GPLs) and surrounded by two piezoelectric layers. Various sources of uncertainties related to the material properties, the geometry of the reinforcements, and piezoelectric parameters are considered in this study. The uncertainty propagations in the nonlinear dynamic responses of the shells are examined for different variations of GPL dispersions and porosity distributions in the core. For this purpose, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the thickness direction. In order to investigate the uncertainty propagation in the responses of the shells, the interval analysis method which is an appropriate technique for the uncertainty analysis of systems with bounded uncertainties is utilized. The Halpin-Tsai model is used to find the effective properties of the GPL-reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders’ nonlinear theory. In order to solve the equations of motion and to obtain the dynamic responses of the shells, the Fourier differential quadrature (FDQ) technique is employed. According to the analysis results, the sensitivities of the responses of internal moment, displacement, and internal force have the highest values relative to the uncertainty sources, respectively, whereas the uncertainty percentages for the responses of displacement, internal moment, and internal force respectively have the highest values for the examined loads.

Semi-analytical model of an acoustic black hole piezoelectric bimorph cantilever for energy harvesting

An acoustic black hole (ABH) beam termination can be achieved by decreasing its thickness according to a power-law profile. Waves entering the ABH slow down and vibrational energy strongly concentrates at the tip of the beam. This can be exploited for energy harvesting, as suggested in some recent works. The finite element method (FEM) is commonly used to carry out the simulations, which hampers long parametric analyzes. In this paper, we develop a semi-analytical approach to characterize the performance of a piezolectric bimorph cantilever with an ABH termination. The method can be easily extended to further configurations and allows one to determine ABH harvesting capabilities when varying system parameters, in a fast and efficient way. The Lagrangian of the ABH beam plus piezoelectric layers is constructed and the coupled equations for the flexural vibrations and voltage are derived from it. The flexural displacement field is expanded in terms of Gaussian basis functions. Vibration shapes and harvested power are computed with the proposed method and validated against FEM simulations. The ABH piezolectric bimorph cantilever is shown to substantially enhance the harvesting capabilities of a cantilever with uniform cross-section. The semi-analytical approach is then used to examine the influence of several ABH and piezoelectric layer parameters on energy harvesting efficiency. As regards the former, the effects of the tip truncation thickness and ABH order are explored. In what concerns the piezoelectric layer, we investigate the effects of its location, thickness, splitting it into several patches and varying the load resistors to enhance its performance in a broad frequency range. The proposed method constitutes a valuable tool for the design of ABH energy harvesting devices.

Piezoelectric Energy Harvester Based on LiNbO3 Thin Films.

This paper reports the results of the influence of the energy of laser pulses during laser ablation on the morphology and electro-physical properties of LiNbO3 nanocrystalline films. It is found that increasing laser pulse energy from 180 to 220 mJ results in the concentration of charge carriers in LiNbO3 films decreasing from 8.6 × 1015 to 1.0 × 1013 cm−3, with the mobility of charge carriers increasing from 0.43 to 17.4 cm2/(V·s). In addition, experimental studies of sublayer material effects on the geometric parameters of carbon nanotubes (CNTs) are performed. It is found that the material of the lower electrode has a significant effect on the formation of CNTs. CNTs obtained at the same growth time on a sample with a Cr sublayer have a smaller diameter and a longer length compared to samples with a V sublayer. Based on the obtained results, the architecture of the energy nanogenerator is proposed. The current generated by the nanogenerator is 18 nA under mechanical stress of 600 nN. The obtained piezoelectric nanogenerator parameters are used to estimate the parameters of the hybrid-carbon-nanostructures-based piezoelectric energy converter. Obtained results are promising for the development of efficient energy converters for alternative energy devices based on lead-free ferroelectric films.

Novel lead-free composites with two porosity levels: large piezoelectric anisotropy and high sensitivity

A novel lead-free 1–3-type composite based on a ferroelectric domain-engineered single crystal is put forward. In the porous polymer matrix of this composite, two different porous structures are observed, and the effect of these structures on the piezoelectric performance, electromechanical coupling and related anisotropy parameters of 1–3-type composites is first studied. New diagrams that link the volume fractions of the single-crystal component and the porous regions in the polymer medium are built to show validity of conditions for a large anisotropy of piezoelectric coefficients and electromechanical coupling factors , and . In the composites based on the complex alkali niobate alkali tantalate single crystal with small piezoelectric anisotropy (/|| = 2.1), the three anisotropy factors /|| ≥ 5, /|| ≥ 5 and /|| ≥ 5 hold simultaneously due to the presence of layers with heavily prolate and heavily oblate air pores in the porous polymer matrix. The two porosity levels influence the elastic anisotropy of the porous matrix, and this leads to an increase in the three anisotropy factors across wide volume-fraction ranges. Of independent interest is the high piezoelectric sensitivity of the composites for which the condition ≥1 V m N−1 holds at their piezoelectric coefficient ≈ (200–500) pC N−1 and electromechanical coupling factors ≈ ≈ 0.8–0.9. The studied parameters of the novel piezo-active 1–3-type composites are of value for various applications such as active elements of piezoelectric transducers, energy-harvesting devices and sensors.

Dynamic anti-plane behavior for a semi-infinite piezoelectric medium with a locally debonded cylindrical inclusion near the surface

The problem of dynamically debonded cylindrical inclusion near the interface of semi-infinite piezoelectric materials was theoretically investigated. The effects of different geometric and physical parameters on the dynamic stress intensity factor (DSIF) of the crack tip are discussed. The theoretical expressions for the crack (debonding) DSIF were obtained using methods that included Green’s function, the complex variable function, and multipolar coordinates, and the numerical results showed that the dynamic characteristics of the debonded structure were more obvious under conditions of low frequency and large piezoelectric characteristic parameters. In addition, the period of the DSIF at the crack tip became shorter as the incident wave number increased. There are, therefore, important theoretical and engineering considerations for the dynamic analysis of piezoelectric materials with debonded cylindrical inclusion.

A PMN-PT Composite-Based Circular Array for Endoscopic Ultrasonic Imaging.

Endoscopic ultrasound (EUS), an interventional imaging technology, utilizes a circular array to delineate the cross-sectional morphology of internal organs through the gastrointestinal (GI) track. However, the performance of conventional EUS transducers has scope for improvement because of the ordinary piezoelectric parameters of Pb(Zr, Ti) [Formula: see text] (PZT) bulk ceramic as well as its inferior mechanical flexibility which can cause material cracks during the circular shaping process. To achieve both prominent imaging capabilities and high device reliability, a 128-element 6.8-MHz circular array transducer is developed using a Pb(Mg [Formula: see text]Nb [Formula: see text]) [Formula: see text]-PbTiO3 (PMN-PT) 1-3 composite with a coefficient of high electromechanical coupling ( [Formula: see text]) and good mechanical flexibility. The characterization results exhibit a large average bandwidth of 58%, a high average sensitivity of 100 mVpp, and a crosstalk of less than -37 dB near the center frequency. Imaging performance of the PMN-PT composite-based array transducer is evaluated by a wire phantom, an anechoic cyst phantom, and an ex-vivo swine intestine. This work demonstrates the superior performance of the crucial ultrasonic device based on an advanced PMN-PT composite material and may lead to the development of next-generation biomedical ultrasonic devices for clinical diagnosis and treatment.

Frequency dependences of complex constants of lead-free ferroelectric ceramics

In this work, the frequency dependences of complex piezoelectric, dielectric, and elastic parameters of lead-free ferroelectric ceramics based on solid solutions of the (Na, Li)NbO3 system were studied in the frequency range up to 100 MHz. A complete set of complex parameters of lead-free ferroelectric ceramics was measured using the PRAP automatic iterative method. It was shown that the studied lead-free ferroelectric ceramics are characterized by low attenuation of ultrasonic waves and lack of dispersion in a wide frequency range, and can be used in high-frequency ultrasonic transducers for medical and nondestructive testing equipment.

Method of electromechanical characterization of ferroelectric materials

The article presents a new method of electromechanical characterization of ferroelectric materials. The measurements of the complex elastic, electromechanical, and piezoelectric parameters of ferroelectric ceramics were fulfilled using the piezoelectric resonance analysis method. To study nonlinear processes occurring in ferroelectric ceramics under the external influences the dc electric field, dependencies of the complex electromechanical parameters of the PZT type piezoceramics were measured and analyzed.

Application of the impedance spectroscopy method for the study of relaxation processes in ferroelectric ceramics

In this paper, the study of relaxation processes in ferroelectric ceramics under the influence of a dc electric field has been performed. To measure the field and time dependences of the complex elastic, dielectric, and piezoelectric parameters of ferroelectric ceramics, the impedance spectroscopy method and piezoelectric resonance analysis program were used. A comparative analysis of various characterization methods was carried out, and a physical interpretation of the results has been proposed.

Diphenylalanine-Derivative Peptide Assemblies with Increased Aromaticity Exhibit Metal-like Rigidity and High Piezoelectricity.

Diphenylalanine (FF) represents the simplest peptide building block that self-assembles into ordered nanostructures with interesting physical properties. Among self-assembled peptide structures, FF nanotubes display notable stiffness and piezoelectric parameters (Young’s modulus = 19–27 GPa, strain coefficient d33 = 18 pC/N). Yet, inorganic alternatives remain the major materials of choice for many applications due to higher stiffness and piezoelectricity. Here, aiming to broaden the applications of the FF motif in materials chemistry, we designed three phenyl-rich dipeptides based on the β,β-diphenyl-Ala-OH (Dip) unit: Dip-Dip, cyclo-Dip-Dip, and tert-butyloxycarbonyl (Boc)-Dip-Dip. The doubled number of aromatic groups per unit, compared to FF, produced a dense aromatic zipper network with a dramatically improved Young’s modulus of ∼70 GPa, which is comparable to aluminum. The piezoelectric strain coefficient d33 of ∼73 pC/N of such assembly exceeds that of poled polyvinylidene-fluoride (PVDF) polymers and compares well to that of lead zirconium titanate (PZT) thin films and ribbons. The rationally designed π–π assemblies show a voltage coefficient of 2–3 Vm/N, an order of magnitude higher than PVDF, improved thermal stability up to 360 °C (∼60 °C higher than FF), and useful photoluminescence with wide-range excitation-dependent emission in the visible region. Our data demonstrate that aromatic groups improve the rigidity and piezoelectricity of organic self-assembled materials for numerous applications.

Interfacial cracks near an eccentric circular hole in piezoelectric bi-materials subjected to dynamic incident anti-plane shearing

Dynamic fracture analysis of piezoelectric materials with eccentric defects is an important criterion for the design of piezoelectric components. This work aims to suggest an effective method for the dynamic anti-plane shearing problem of piezoelectric bi-materials with permeable interfacial cracks near an eccentric circular hole. In the paper, Fredholm’s equations are solved via the Green’s function method and the coordinate transformation method. Based on conjunction and crack-deviation techniques, the dynamic stress intensity factors (DSIFs) at the outer and the inner tips of the left crack are expressed analytically. As cases, the effects of the eccentric distance, the piezoelectric parameters, the ratio of the crack length to the hole radius, and the dimensionless wave number of the incident wave are presented graphically.

The Effect of Mixed Doping on the Microstructure and Electrophysical Parameters of the Multicomponent PZT-Type Ceramics.

This work shows the influence of admixture on the basic properties of the multicomponent PbZr1−xTixO3 (PZT)-type ceramics. It presents the results of four compositions of PZT-type material with the general chemical formula, Pb0.99M0.01((Zr0.49Ti0.51)0.95Mn0.021Sb0.016W0.013)0.9975O3, where, in the M position, a donor admixture was introduced, i.e., samarium (Sm3+), gadolinium (Gd3+), dysprosium (Dy3+) or lanthanum (La3+). The compositions of the PZT-type ceramics were obtained through the classic ceramic method, as a result of the synthesis of simple oxides. The X-ray diffraction (XRD) pattern studies showed that the obtained multicomponent PZT materials have a tetragonal structure with a P4mm point group. The microstructure of the obtained compositions is characterized by a well crystallized grain, with clearly visible grain boundaries. The composition with the admixture of lanthanum has the highest uniformity of fine grain microstructure, which positively affects its final dielectric and piezoelectric properties. In the multicomponent PZT-type ceramic, materials utilize the mixed (acceptor and donor) doping of the main compound. This dopiong method has a positive effect on the set of the electrophysical parameters of ceramic materials. Donor dopants W6+ (at positions B) and M3+ = Sm3+, Gd3+, Dy3+, and La3+ (at positions A) increase the dielectric and piezoelectric properties, while the acceptor dopant Sb3+ (at positions B) increases the time and temperature stability of the electrophysical parameters. In addition, the suitable selection of the set of admixtures improved the sinterability of the ceramic samples, as well as resulted in obtaining the required material with good piezoelectric parameters for the poling process. This research confirms that all ceramic compositions have a set of parameters suitable for applications in micromechatronics, for example, as actuators, piezoelectric transducers, and precision microswitches.

Energy harvesting of two inverted piezoelectric flags in tandem, side-by-side and staggered arrangements

The flow-induced vibration characteristics and energy extraction performance of flexible inverted piezoelectric flags in a uniform flow are studied by using an immersed boundary-lattice Boltzmann method for Reynolds number of 100, mass ratio of 2.9 and non-dimensional bending stiffness of 0.26 which correspond to the maximum flapping amplitude for a single inverted flag. The coupled fluid-structure-electric dynamics of two inverted piezoelectric flags in the tandem, side-by-side and staggered arrangements is investigated to determine the effects of the piezoelectric parameters (α and β) on the dynamics of the flags and to quantify the energy harvesting performance. Simulations are conducted by varying the streamwise gap distance (Gx/L) from 0.1 to 3.2 and cross-stream gap distance (Gy/L) from 0.4 to 2.5. It is found that both the flapping amplitude and the frequency of the flags reduce as the piezo-mechanical coupling parameter (α) increases due to the damping effect, particularly in the tandem arrangement. The maximum electrical power coefficient (C¯P) is produced in the staggered arrangement at α=0.5, β (piezo-electric tuning parameter) = 1.5, Gx/L=1.4 and Gy/L=2.2 where the C¯P of the downstream flag is 0.042, 16% and 12.5% higher than that of the upstream flag and that of the single flag, respectively. The improvement in C¯P of the downstream flag is attributed to the increase in the kinetic energy of the fluid flow created by the upstream flag as a bluff body.

Impact of point source and mass loading sensitivity on the propagation of an SH wave in an imperfectly bonded FGPPM layered structure

The aim of the present study is to analyze the propagation behavior of an SH wave in a layered structure constituted of a functionally graded piezo-poroelastic material (FGPPM) layer imperfectly bonded to an FGPPM half-space influenced by a stress point source of disturbance situated at the interface. Mass loading sensitivity of the considered structure is also analyzed by assuming a deposition of an infinitesimally thin layer at the free surface. A mathematical model for mechanical and electrical dynamics of the said material is developed for both considered structures in distinct cases. Appropriate Green’s functions for both layer and half-space are derived by using admissible boundary conditions. The dispersion relation of an SH wave is obtained for both cases, and the obtained results are also validated with classical results of Love wave. The impact of various influencing parameters like functional gradient parameters, imperfectness parameter, piezoelectric coupling parameter, and piezo-porous coupling parameter on the phase velocity of an SH wave is analyzed graphically for a BaTiO$$_3$$-crystal layer and PZT-5H half-space. Moreover, for the case of the mass loading sensitivity, the influencing parameters are also studied for the deposition of a sensitive ZnO layer. Variation of group velocity with wave number is also sketched out graphically.

Electromechanical Model of Coupling Spring Piezoelectric Oscillator with Loading

The paper studies the influence of piezoelectric materials and structural parameters on the electromechanical conversion characteristics of the piezoelectric vibrator. Employing the mechanical theory of Euler–Bernoulli beam, the mechanical vibration and circuit balance equation are obtained about the single-step variable cross-section bimorph piezoelectric vibrator under the condition of external resistance, and the analytical equations are derived for the displacement, output voltage, and conversion efficiency of the piezoelectric vibrator excited by near natural frequency simple harmonic support. The validity of the theoretical model is verified by vibration test. Theoretical analysis and experimental results show that the mechanical and electrical conversion efficiency of the piezoelectric vibrator is the highest when the circuit impedance is matched, and the mechanical and electrical conversion efficiency of the piezoelectric vibrator is determined by the resistance ratio caused by mechanical and electrical coupling after resistance optimization.

DC bias electric field and stress dependence of piezoelectric parameters in lead zirconate titanate ceramics – Phenomenological approach

The piezoelectric material behavior, including loss mechanism, under external DC electric field and stress biases have been extensively studied in lead zirconate titanate ceramics. However, in order to achieve a better understanding of these effects, development of a comprehensive model is required. The purpose of this paper is to develop a phenomenological model to explain the nonlinear nature of piezoelectric parameters under DC bias electric field and stress. Therefore, the Landau-Devonshire energy function considering external biases was developed and accordingly the material properties were derived, based on first order approximation. In order to explain the compliance and piezoelectric constants change higher order elastic and electrostrictive terms were introduced into the Gibb's free energy function.Accordingly, thermodynamic theory parameters, including higher order parameters, of a soft PZT were measured and characterized based on inverse permittivity behavior near Curie temperature. Finally, the phenomenological model predictions of material property changes under DC bias electric field and compressive stress were compared with experimental data reported by our group. The proposed model succeeded to explain the material properties change under external biases. Furthermore, the effect of DC electric field and compressive stress on loss parameters were explained based on domain wall motion.