Electrical Boundary Conditions Research Articles

Characteristics of complete circumferential guided wave in a piezoelectric semiconductor cylindrical shell

In this paper, the characteristics of circumferential Lamb-like wave in a cylindrical shell of N-type piezoelectric semiconductor are investigated by employing the analytic Legendre orthogonal polynomial method (ALOPM). Based on the linear phenomenological theory, the governing differential equations are derived for different electrical boundary conditions, and transformed into a matrix eigenvalues problem via using the ALOPM. The dispersion solutions for a piezoelectric semiconductor cylindrical shell with big radius-thickness ratio obtained from the ALOPM are verified by comparing with the results from the global matrix method (GMM). Three-dimensional spectrum is plotted for a better observation. The spectrum of piezoelectric semiconductor is symmetrically distributed about the frequency axis, which is different from the piezoelectric dielectric material. The effects of different electrical boundary conditions, steady-state carrier density and radius-thickness ratio on phase velocity dispersion curves are illustrated. The amplitude distributions of displacement, electric potential and perturbation of the carrier density are studied. The effects of steady-state carrier density on the stress distribution are also illustrated. Non-propagating wave modes with low attenuation and high phase velocity value are found. The corresponding results presented in this work can be used to optimize the design of piezoelectric semiconductor acoustic wave devices.

On the Enforcement of Electric Field Boundary Condition in the Moment Method Solution of Volume-Surface Integral Equation

When the volume-surface integral equation (VSIE) is used to model the composite objects, the electric field boundary condition (BC) can be explicitly enforced on the dielectric-perfect electric conductor (PEC) interfaces to reduce the volumetric unknowns. In the proposed BC-based VSIE, using the least-square method, one of the four coefficients of SWG basis functions belonging to a same tetrahedron terminated by a PEC triangle is directly calculated by the other three, which is no longer a volumetric unknown. The matrix equation generated by the method of moments is iteratively solved in a straightforward manner, which can be accelerated by the multilevel fast multipole algorithm. Through reliable numerical results, it is illustrated that the enforcement of the BC can reduce the memory usage and the number of iterations without compromising accuracy, in addition to good versatility.

Giant voltage amplification from electrostatically induced incipient ferroelectric states

Ferroelectrics subject to suitable electric boundary conditions present a steady negative capacitance response1,2. When the ferroelectric is in a heterostructure, this behaviour yields a voltage amplification in the other elements, which experience a potential difference larger than the one applied, holding promise for low-power electronics3. So far research has focused on verifying this effect and little is known about how to optimize it. Here, we describe an electrostatic theory of ferroelectric/dielectric superlattices, convenient model systems4,5, and show the relationship between the negative permittivity of the ferroelectric layers and the voltage amplification in the dielectric ones. Then, we run simulations of PbTiO3/SrTiO3 superlattices to reveal the factors most strongly affecting the amplification. In particular, we find that giant effects (up to tenfold increases) can be obtained when PbTiO3 is brought close to the so-called ‘incipient ferroelectric’ state.

Size-dependent and piezoelectric effects on SH wave propagation in functionally graded plates

This paper is concerned with the propagation of shear horizontal waves in a functionally graded piezoelectric small-scaled plate. In the context of the modified couple stress theory, the Legendre orthogonal polynomial method is utilized to derive the solutions based on the explicit functionally graded model. Four different electric boundary conditions are considered. The obtained results are compared with those by the global matrix method and the advantages of the polynomial method are indicated. Furthermore, the couple stress effect and piezoelectric effect on the SH waves are investigated. Numerical results indicate that the couple stress and piezoelectric coupling effects on SH propagation are mutually inhibited.

Tunable asymmetric transmission of Lamb waves in piezoelectric bimorph plates by electric boundary design

The multi-mode and dispersion natures of elastic guided waves bring big challenges for wave manipulation, and also provide more possibilities for smart device design. In this study, a piezoelectric bimorph plate connected to a periodic arrangement of electric circuits is proposed, and both propagating and evanescent guided Lamb waves are investigated through the complex band structure resulting form using different shunting capacitor or inductor distributions. Results show that keeping and breaking the symmetry of the electric boundary condition can, respectively, lead to decoupling or hybridizing of multi-mode Lamb waves. Accordingly, the asymmetric transmission at a desired frequency can be realized by combining the symmetric and asymmetric electric boundary conditions. Harmonic analysis shows that numerical results are in good agreement with the prediction of complex band structure. Actively changing the electric boundary conditions can be used for guided wave propagation in piezoelectric bimorph plates to easily control the system without changing the structure’s geometry. The framework presented herein offers enhanced capabilities for controlling guided wave propagation for engineering applications and to develop nondestructive testing techniques.

A phase field model for fatigue fracture in piezoelectric solids: A residual controlled staggered scheme

Prediction of the fatigue life of piezoelectric devices and structures is of scientific and engineering significance. In this work, a phase field model for fatigue fracture in piezoelectric materials is developed by means of the Hamilton principle. Two classical phase field fracture models are unified in the present framework. A cumulative history variable is introduced to quantify the degradation of the fracture toughness under cyclic loading. The proposed model accounts for three representative electric boundary conditions on crack faces describing the fatigue fracture behaviors in different physical situations. The residual controlled staggered scheme is extended to address the fatigue fracture problems in the context of electro-elasticity. The present algorithm overcomes the convergence problem for the monolithic approach and shows higher accuracy with lower computational effort in comparison to the single-pass staggered scheme. Systematic numerical simulations are carried out in 2D and 3D cases. The effects of the electric boundary condition, external electric field, and the geometry of the crack tip on the fatigue fracture behaviors of piezoelectric solids have been discussed. The effect of the electric boundary conditions on the fatigue life varies depending on the direction of the external electric field. The present work is beneficial to assess the lifetimes of piezoelectric devices in practical applications.

Hygrothermal Buckling of Smart Graphene/Piezoelectric Nanocomposite Circular Plates on an Elastic Substrate via DQM

This paper aims to study the hygrothermal buckling of smart graphene/piezoelectric circular nanoplates lying on an elastic medium and subjected to an external electric field. The circular nanoplates are made of piezoelectric polymer reinforced with graphene platelets that are uniformly distributed through the thickness of the nanoplate. The material properties of the nanocomposite plate are determined based on the modified Halpin-Tsai model. To capture the nanoscale effects, the nonlocal strain gradient theory is applied. Moreover, the principle of virtual work is employed to establish the nonlinear stability equations in the framework of classical theory. The differential quadrature method is utilized to solve the governing equations. Among the important aims of the paper is to study the influences of various parameters such as graphene weight fraction, elastic foundation parameters, external applied electric field, humid conditions, and boundary conditions on the thermal buckling of the smart nanocomposite circular nanoplates. It is found that the increase in graphene components and elastic foundation stiffness enhances the strength of the plates; therefore, the buckling temperature will increase.

Transfer matrix model and experimental validation for the integrated piezo longitudinal actuators

The housing and pre-compressed spring of the integrated piezo longitudinal actuator can protect the piezoelectric stack from shear stress and tensile stress. In this paper, the limitations of this actuator model in existing vibration control projects are pointed out. An electromechanical coupling dynamic model in the transfer matrix form is established for the longitudinal vibration of the integrated piezo longitudinal actuator. The model includes all parameters of the integrated piezo longitudinal actuator: force and velocity at both ends, material and structural parameters, voltage and current, which is suitable for any mechanical and electrical boundary conditions; The transfer matrix method has a simple structure and clear physical definition, which is convenient to be applied to the vibration control system. This model is verified by the finite element software and experiments. In the experimental verification, an electromechanical coupling dynamic experiment system of the integrated piezo longitudinal actuator is established. The accuracy of this model is verified by comparing the frequency domain dynamic response of various parameters in the simulation and experiments. The integrated piezo longitudinal actuator model provides a wide range of possibilities for model-based controller design, active and semi-active control, electric power estimation, and optimal vibration isolation performance estimation.

Structural design and experimental analysis for AlN Lamb-wave resonators with different electrical boundary conditions

This paper presents an Aluminum Nitride (AlN) Lamb-wave resonator with high series-resonance quality factors (Qs) and good spectral purity. The influence of the interdigitated (IDT) electrode width and electrical boundary condition was theoretically analyzed to improve effective electro-mechanical coupling coefficient (k2eff) and spectral purity. According to the structural characteristic of the designed resonators, an advanced micro-manufacturing process was designed. A thermal oxide layer was employed to avoid the etching of inactive regions, which contributes to achieving the high Qs and high-yield fabrication. The measured results show the IDT-ground resonators with 12 μm and 6 μm electrode periods exhibit Qs values as high as 4457.1 and 2625.1, and k2eff of 0.61% and 0.33%, respectively. The IDT-IDT resonators have higher k2eff, but their Qs values are severely attenuated. Through observing their section morphologies, the measured shear angles of the bottom IDT electrodes with 12 μm and 6 μm periods are 54.95° and 65.7° respectively, and the surface AlN film has tiny cracks, which induces the performance deterioration of the IDT-IDT resonators. Moreover, the influence of the IDT material on the resonator’s performance was also analyzed.

Finite element analysis of the magnetoelectric effect on hybrid magnetoelectric composites

The multi-component hybrid magnetoelectric (ME) composites obtained by using high molecular polymer as the first component and ferromagnetic or ferroelectric material as the second component by hierarchical compounding has the advantages of light weight, easy processing and flexibility. It has the characteristics of good performance and can also realize the conversion between magnetic energy and electric energy, which has potential applications in the fields of bionic robots and medical non-invasive detection. In this study, the finite element method is used to study its ME effect. Considering the distribution characteristics of the component materials and their nonlinear constitutive equations, as well as the dynamic equation and the corresponding mechanical and electrical boundary conditions, a finite element model of the ME effect of the ME composites is established. The distribution of elastic field, magnetic field and electric field of the hybrid ME composites were studied, and the influence of microstructural distribution characteristics, geometric parameters, external magnetic field, temperature and other factors on its magnetoelectric coefficient was analyzed. The calculated results can provide the theoretical guidance for the optimal design of high-performance magnetoelectric devices and render better support for the technological development in the field of magnetoelectricity.

Fatigue crack growth mechanism in ferroelectric ceramics under alternating electric field: An investigation by digital image correlation technique

The deformation of crack tip in PZT ceramics under cyclic electric field loading was characterized by Digital Image Correlation (DIC) technique. Two other specimens without speckles were used to observe the physical processes during the crack propagation in-situ. The deformation of the region of interest is elucidated. Near the U-shaped notch, the DIC results directly reveal the existence of incompatible deformation. However, in the front of the newly formed crack, no incompatible deformation was observed. Additionally, in-situ observation reveals that, the crack growth occurs at the stage of crack closure when the crack propagates steadily. The observed pop-in behavior of the crack during the first cycle of electric field loading is rationalized by the interaction between the incompatible domain switching zones with and without U-shaped notch, which is consistent with the explanation of Westram et al. The subsequent crack propagation after the pop-in cannot be rationalized by the model exploited by Zhu and Yang, Westram et al., and Liu and Fang, which is thought to be related to three different factors – arcing, wedging and grain-to-grain interaction. The mechanism for the appearance and the disappearance of the incompatible domain switching zone near the U-shaped notch and around the tip of the newly formed crack is discussed based on the electrical boundary condition (EBC) of the crack surfaces we proposed recently.

Surface charge and thermal dependence of energy conversion in nanochannels

Micro/nanofluidics based energy conversion has drawn much attention in recent years. In this work, an ion transport model driven by pressure and temperature gradient is proposed to investigate the energy conversion characteristic in nanochannels. The results illustrate that the power generation performance under the different electrical boundary conditions exhibit a significant deviation. The output power is weakened at low and high solution concentrations/pH values, the maximum output power is corresponding to 5% and 50% deviation, respectively. And it is improved with the increasing temperature and pressure gradient due to the significant enhanced current. Especially, the maximum output power of 720 nW/m is obtained when the temperature difference is 20 °C and pressure gradient is 0.025 MPa/μm, which is corresponding to 21% enhancement than isothermal condition. Besides, we found that the Soret effect plays an important role on ion transport and the viscous dissipation effect can be neglected. The obtained results offer the valuable information for the performance optimization in micro/nanofluidic based energy devices.

Size dependent torsional electro-mechanical analysis of flexoelectric micro/nanotubes

The free vibration and static torsion of a coupling electromechanical flexoelectric micro/nanotube have been investigated, in the present study. Using the non-classical theory of continuum mechanics which is based on a strain gradient, the coupling governing equations of torsional flexoelectric micro/nanotubes have been developed. To derive the coupling governing equations the variational method has been used and the formulation with the classical and non-classical boundary conditions is generally derived for torsional flexoelectric micro/nanotubes. For the first time, the formulation of micro/nanotube torsional flexoelectric coupling with independent polarization effect is presented in this paper which can be used for specific applications. At last, the static analysis and free vibrations results are presented for specific mechanical and electrical boundary conditions. The parameter of mechanical and electrical size effect changes has a great effect on the results. However, the effect of the mechanical and electrical size effect parameter on direct flexoelectric torsion is also opposite, but the effect of mechanical and electrical size effect parameter on reverse flexoelectric torsion is similar. Polarization is also introduced as a new variable in the equations and its effect is investigated as an independent variable of the electric field in the results, in this paper. As a significant parameter, the results show that polarization plays an important role to simulate the torsional electromechanical structures.

Convert Widespread Paraelectric Perovskite to Ferroelectrics.

While nature provides a plethora of perovskite materials, only a few exhibit large ferroelectricity and possibly multiferroicity. The majority of perovskite materials have the nonpolar CaTiO_{3}(CTO) structure, limiting the scope of their applications. Based on the effective Hamiltonian model as well as first-principles calculations, we propose a general thin-film design method to stabilize the functional BiFeO_{3}(BFO)-type structure, which is a common metastable structure in widespread CTO-type perovskite oxides. It is found that the improper antiferroelectricity in CTO-type perovskite and ferroelectricity in BFO-type perovskite have distinct dependences on mechanical and electric boundary conditions, both of which involve oxygen octahedral rotation and tilt. The above difference can be used to stabilize the highly polar BFO-type structure in many CTO-type perovskite materials.

Tuning the resonance frequency of piezoelectric energy harvesters by applying direct current electric field on piezoelectric elements

Different from previous strategies utilized to improve the energy conservation efficiency of piezoelectric energy harvesters (PEHs) from the environment, by broadening the frequency-bandwidth of energy harvesters using a specifically designed structure or tuning their resonance frequency (RF) through changing the geometrical/dynamical constraints, we report a method—by applying a direct current (DC) electric field on piezoelectric elements—to tune the RF of PEH based on the phenomenon that the elastic parameters of piezoelectric material are related to its electric field boundary condition. The results of a confirmatory experiment revealed that with a pre-loading DC electric field of −0.5 to 0.75 kV/mm, the RF of a piezoelectric cantilever energy harvester can be tuned from 144 to 156 Hz. The effectiveness of this strategy was further verified by comparing the energy conservation output of the PEH at a frequency that deviates from its RF, and at the same frequency, with pre-loading DC electric field adjustment.

Effects of Convective Boundary Condition and Activation Energy on Chemically Reacting Nanofluid Flow with Radiation

The combined impact of activation energy and radiation on the magnetohydrodynamic flow of nanofluid near a stagnation point with the electric field and convective boundary conditions are exposed in this study. By using similarity transformations, the non-linear partial differential equations renewed into non-linear ODEs. The resultant non-linear ODEs were solved numerically by using a shooting scheme. The impact of non-dimensional parameters on temperature, velocity, solute concentration, and nanoparticle volume fraction profiles are discussed graphically. The velocity and solute concentration increased by increasing the activation energy.

Higher-order accurate finite-difference simulation for tunnel propagation modeling

PurposeThis paper aims to improve the computational efficiency of higher-order accurate Noye–Hayman [NH (9,9)] implicit finite difference scheme for the solution of electromagnetic scattering problems in tunnel environments.Design/methodology/approachThe proposed method consists of two major steps: First, the higher-order NH (9,9) scheme is numerically discretized using the finite-difference method. The second step is to use an algorithm based on hierarchical interpolative factorization (HIF) to accelerate the solution of this scheme.FindingsIt is observed that the simulation results obtained from the numerical tests illustrate very high accuracy of the NH (9,9) method in typical tunnel environments. HIF algorithm makes the NH (9,9) method computationally efficient for two-dimensional (2D) or three-dimensional (3D) problems. The proposed method could help in reducing the computational cost of the NH (9,9) method very close to O(n) usual O(n3) for a full matrix.Research limitations/implicationsFor simplicity, in this study, perfect electric conductor boundary conditions are considered. Future research may also include the utilization of meteorological techniques, including the effects of backward traveling waves, and make comparisons with the experimental data.Originality/valueThis study is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.

Electrical boundary condition at the crack surface in ferroelectrics

AbstractElectrical boundary condition (EBC) at the crack surface has significant influence on the fracture behavior of ferroelectrics. Here, we characterized the electrical displacement (ED) response of ferroelectrics specimens with through cracks under cyclic electric field. The physical processes occurred between the crack surfaces are in situ observed. It is found that when the distance between the crack surfaces was smaller than a critical value, significant ED was measured, which cannot be rationalized by the previous EBCs. The appearance of bubbles and arcing between the crack surfaces demonstrates that dielectric breakdown occurs during electric field loading. These results imply that the EBC of the crack surface is permeable, and the dielectric breakdown process should be taken into consideration.

Bandgap and mode shape tuning of piezoelectric metamaterial

The mode shape of piezoelectric metamaterials is tuned by manipulating spatially the electrical boundary conditions of the piezo-elements, in a desired and controlled manner, in order to tailor the wave propagation characteristics through these metamaterials. The proposed concept relies on the fact that open-circuit piezo-elements made of lead-zirconate-titanate (PZT4) are twice as stiff as the same piezo-elements when operating under short-circuit conditions. Appropriate switching of the boundary conditions of the different piezo-elements between open and short-circuit conditions results in any desirable spatially distribution of the stiffness over the entire metamaterial volume. With such capabilities, it would be possible to control the bandgap characteristics of the metamaterial. But, more importantly, it would also be feasible to alter the mode shape characteristics of the metamaterial in order to control the magnitude and direction of wave propagation. This in effect enables controlling or breaking the reciprocity characteristics of the metamaterial. A finite element model (FEM) is developed to model the bandgap and mode shape characteristics of one-dimensional piezo-metamaterial. The effect of various switching strategies on the location and spectral width of the bandgap characteristics is illustrated. Furthermore, the switching strategies are also shown to influence the mode shapes, energy flow, and reciprocity characteristics of the piezo-metamaterial.

Thickness-Stretch Vibration of an Infinite Piezoelectric Plate with Flexoelectricity

In this paper, the thickness-stretch vibration of an infinite piezoelectric plate is studied, with consideration of the flexoelectric effect. The theoretical model developed herein is based on a one-dimensional formulation, with the assumption that the displacement and electric potential vary through the thickness. The Gibbs energy density function and variational principle are adopted to derive the constitutive equation with flexoelectricity, governing equations, and boundary conditions. For the effect of flexoelectricity, the coupling between the strain gradient through the thickness and the electric field is considered. Two electric boundary conditions are used in this work and the corresponding frequency shift due to the flexoelectricity is calculated. The present results demonstrate that the flexoelectric effect decreases the fundamental frequency of the thickness-stretch vibration and has a significant effect on the vibrational frequencies of the thickness-stretch mode of a thin piezoelectric plate. The results also show that the flexoelectric effect has a significant size dependency, and should be taken into consideration for the design and development of next-generation high-precision and high-frequency piezoelectric transducers and resonators in the future.