Electrical Boundary Conditions Research Articles

Love-Type Wave in PMN-PT Single Crystal Layered Structures with Periodic Undulations

Love-type wave propagation has been studied in a layered structure consisting of a thin layer of PMN-PT single crystal deposited on an elastic half-space. The weakly periodic undulations of the upper surface of the layered system and the common interface between the PMN-PT layer and the elastic substrate are considered. The PMN-PT single crystal is poled along the [011]_c direction so that the macroscopic symmetry is orthonormal mm2. The dispersion relations for electrically open and shorted circuits are obtained. The effects of various parameters including corrugation, undulatory, position and electrical boundary conditions on dispersion properties of Love-type waves are discussed. The results show that corrugations of the surface and the interface play a dominant role in the propagation of a Love-type wave, especially, the interfacial corrugation can produce an anomalous dispersion in the case of an electrically shorted condition. The surface corrugation enhances the phase velocity of a Love-type wave while the interface corrugation reduces the phase velocity in the range of relatively smaller wavenumber, and these variations gradually tend to vanish with increase in wavenumber. The undulatory parameter and the position parameter present a secondary impact on the dispersion behaviors of a Love-type wave compared with the corrugation parameters, both of them slightly enhance the phase velocity. The obtained results can offer some fundamentals for improving the efficiency and sensitivity of the interface response in the design and application of piezoelectric SAW devices.

Numerical and Experimental Investigation of the Design of a Piezoelectric De-Icing System for Small Rotorcraft Part 1/3: Development of a Flat Plate Numerical Model with Experimental Validation

The objective of this research project is divided in four parts: (1) to design a piezoelectric actuator-based de-icing system integrated to a flat plate experimental setup and develop a numerical model of the system with experimental validation, (2) use the experimental setup to investigate actuator activation with frequency sweeps and transient vibration analysis, (3) add ice layer to the numerical model and predict numerically stresses for different ice breaking with experimental validation, and (4) bring the concept to a blade structure for wind tunnel testing. This paper presents the first objective of this study. First, preliminary numerical analysis was performed to gain basic guidelines for the integration of piezoelectric actuators in a simple flat plate experimental setup for vibration-based de-icing investigation. The results of these simulations allowed to optimize the positioning of the actuators on the structure and the optimal phasing of the actuators for mode activation. A numerical model of the final setup was elaborated with the piezoelectric actuators optimally positioned on the plate and meshed with piezoelectric elements. A frequency analysis was performed to predict resonant frequencies and mode shapes, and multiple direct steady-state dynamic analyses were performed to predict displacements of the flat plate when excited with the actuators. In those steady-state dynamic analysis, electrical boundary conditions were applied to the actuators to excite the vibration of the plate. The setup was fabricated faithful to the numerical model at the laboratory with piezoelectric actuator patches bonded to a steel flat plate and large solid blocks used to mimic perfect clamped boundary condition. The experimental setup was brought at the National Research Council Canada (NRC) for testing with a laser vibrometer to validate the numerical results. The experimental results validated the model when the plate is optimally excited with an average of error of 20% and a maximal error obtained of 43%. However, when the plate was not efficiently excited for a mode, the prediction of the numerical data was less accurate. This was not a concern since the numerical model was developed to design and predict optimal excitation of structures for de-icing purpose. This study allowed to develop a numerical model of a simple flat plate and understand optimal phasing of the actuators. The experimental setup designed is used in the next phase of the project to study transient vibration and frequency sweeps. The numerical model is used in the third phase of the project by adding ice layers for investigation of vibration-based de-icing, with the final objective of developing and integrating a piezoelectric actuator de-icing system to a rotorcraft blade structure.

Understanding the influence of test specimen boundary conditions on material failure resulting from artificial lightning strike

This paper examines the influence of test specimen boundary conditions on material failure during an artificial lightning strike. A finite element simulation approach is employed which in contrast to an experimental investigation enables the study of material damage during the event.Specimen boundaries, representing the range of conditions found in published experimental works, are examined. Unprotected carbon fibre / epoxy composite material and Society of AutomotiveEngineers (SAE) lightning test Waveform A are studied. Damage predictions with two simulation types (coupled thermal-electric; dynamic, coupled temperature-displacement, explicit) are reported and comparisons made with experimental measurements. The results demonstrate that delamination area is sensitive to specimen boundaries, varying by over 300% for the studied conditions.Thermal damage demonstrates noteworthy interactions between the base and side surface grounding conditions, illustrating the variation of local material thermal loading with boundary condition variation. Both delamination and critical damage depth appear to be independent of mechanical boundaries, whereas the prediction of thermal damage appears highly sensitive to the selection of the specimen electrical potential boundary conditions. This paper, for the first time, establishes the effect of test specimen boundary conditions on material failure, representing a common specimen, with a single material data set and subjected to a single consistent artificial lightning component waveform.

Mesoscale modeling of light transmission modulation in ceramics

We present a modeling approach for simulating and predicting spatially resolved properties of polycrystalline ceramics with coupled optical, elastic and dielectric degrees of freedom. This approach is implemented in the Ferret application, built upon the Multiphysics Object Oriented Simulation Environment (MOOSE) finite-element framework, that allows for the determination of the dependency of optical properties on polycrystalline grain orientation, size, and shape, as well as the action of externally applied electric fields and mechanical distortions. For the evaluation of optical transmission through a polycrystal we adopt a modification of the wave-retardation theory, originally developed by Raman and Viswanathan in 1955. The coupled model produces excellent agreement with experimental results obtained for polycrystalline Al2O3, Ce-doped Y3Al5O12, and ZnS which are used as test cases in this investigation, to evaluate both the visible and infrared parts of the electro-magnetic spectrum. Simulations of the optical properties modulation under different applied mechanical and electrical boundary conditions predict large changes to transmission, including switching from full transparency to opacity in some instances. The results of this investigation highlight a remarkable promise of functional nano- and micro-ceramics for a wide range of advanced engineering applications, including broad spectrum windows with high frequency transparency modulation, and multifunctional metamaterials by design.

Finite element analysis of a thin piezoelectric bimorph with a metal shim using solid direct-piezoelectric and shell inverse-piezoelectric coupling with pseudo direct-piezoelectric evaluation

A thin triple-layer piezoelectric bender, also known as a piezoelectric bimorph with a metal shim, consists of an elastic layer (metal shim) sandwiched between two piezoelectric layers. It is one of the most commonly used piezoelectric composite structures in both sensing and actuation applications. Therefore, this study deals with the coupled piezoelectric-structure interaction analysis of a thin piezoelectric bimorph with a metal shim. In this work, the best features of the solid and shell elements were combined to analyze the piezoelectric and structural fields, respectively, in a thin piezoelectric bimorph with a metal shim. This approach addresses the shortcomings of using a single finite element mesh for both the piezoelectric and structural fields. A transformation method using the block Gauss-Seidel algorithm is employed to exchange the variables between solid direct-piezoelectric and shell inverse-piezoelectric analyses. The metal layer can be analyzed as an elastic body with electrical boundary conditions. A pseudo direct-piezoelectric evaluation method for the metal shim in the piezoelectric analysis is proposed. This method allows us to reuse the existing piezoelectric analysis program, where the metal shim is analyzed as the pseudo direct-piezoelectric material in a single analysis procedure. The homogenization method for the evaluation of bending rigidity and mass is used for modeling the single shell structure in the inverse-piezoelectric analysis of a thin piezoelectric bimorph with a metal layer. Numerical results are given for various electrical configurations of actuators and sensors to validate the present method. Comparison with an exact solution illustrates the accuracy, efficiency, and capability of the developed solid direct and shell inverse-piezoelectric analysis coupled with a pseudo direct-piezoelectric evaluation method to capture the sensor and actuator response of a thin piezoelectric bimorph with a metal shim.

Thermal Conductivities of PZT Piezoelectric Ceramics under Different Electrical Boundary Conditions

<p>Physical properties of polycrystalline lead-zirconate-titanate (PZT) changes according to electrical boundary conditions and poling. This paper reports the thermal properties of poled and unpoled PZT's in the poling direction for open circuit and short circuit conditions. The authors found that the short-circuit condition exhibited the largest thermal conductivity than the open-circuit condition. In the relationship between these two thermal properties, the authors propose the "electrothermal" coupling factor k<sup>κ</sup><sub>33</sub>, which is similar to the electromechanical coupling factor k<sub>33</sub> relating the elastic compliances under short- and open-circuit conditions. On the other hand, the thermal conductivity of the unpoled specimen exhibits the lowest thermal conductivity, in comparison with the poled specimens, which suggests the importance of phonon mode scattering on the thermal conductivity with respect to elastic compliance.</p>

A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains

The overall efficiency and accuracy of standard finite element methods may be severely reduced if the solution of the boundary value problem entails singularities. In the particular case of time-harmonic Maxwell’s equations in nonconvex polygonal domains Ω, H1-conforming nodal finite element methods may even fail to converge to the physical solution. In this paper, we present a new nodal finite element adaptation for solving time-harmonic Maxwell’s equations with perfectly conducting electric boundary condition in general polygonal domains. The originality of the present algorithm lies in the use of explicit extraction formulas for the coefficients of the singularities to define an iterative procedure for the improvement of the finite element solutions. A priori error estimates in the energy norm and in the L2 norm show that the new algorithm exhibits the same convergence properties as it is known for problems with regular solutions in the Sobolev space H2Ω2 in convex and nonconvex domains without the use of graded mesh refinements or any other modification of the bilinear form or the finite element spaces. Numerical experiments that validate the theoretical results are presented.

Electromechanical Vibration Characteristics of Porous Bimorph and Unimorph Doubly Curved Panels

The aim of this study is developing an analytical solution for the free vibration of piezoelectric bimorph and unimorph doubly curved panels with a porous substrate. The panel is assumed to be relatively thick, and the effects of its shear deformation are taken into account. Nonlinear models are considered to describe the variation of mechanical properties and of the electric potential within porous host and piezoelectric layers, respectively. Furthermore, short and open circuit electrical conditions are studied to predict the frequency response for sensing and actuation applications. Employing the first-order shear deformation theory (FSDT), in conjunction with the Hamilton’s variational principle and Maxwell’s equation allows deriving six highly coupled partial differential equations to describe the system dynamics under electromechanical coupling. After analytically solving those equations for simply supported panels, the system frequency response is investigated, for various values of design parameters such as porosity, electrical boundary conditions, and geometry. Moreover, some types of smart panels, including bimorphs and unimorphs layouts, are analyzed. The analysis confirms that the above-mentioned parameters play major roles in the natural frequency response of this system and must be carefully considered in the mechatronic design of this smart structure, although they allow to tailor the system behaviour to the selected application.

Effect of input voltage frequency on the distribution of electrical stresses on the cell surface based on single-cell dielectrophoresis analysis

Electroporation is defined as cell membrane permeabilization under the application of electric fields. The mechanism of hydrophilic pore formation is not yet well understood. When cells are exposed to electric fields, electrical stresses act on their surfaces. These electrical stresses play a crucial role in cell membrane structural changes, which lead to cell permeabilization. These electrical stresses depend on the dielectric properties of the cell, buffer solution, and the applied electric field characteristics. In the current study, the effect of electric field frequency on the electrical stresses distribution on the cell surface and cell deformation is numerically and experimentally investigated. As previous studies were mostly focused on the effect of electric fields on a group of cells, the present study focused on the behavior of a single cell exposed to an electric field. To accomplish this, the effect of cells on electrostatic potential distribution and electric field must be considered. To do this, Fast immersed interface method (IIM) was used to discretize the governing quasi-electrostatic equations. Numerical results confirmed the accuracy of fast IIM in satisfying the internal electrical boundary conditions on the cell surface. Finally, experimental results showed the effect of applied electric field on cell deformation at different frequencies.

Crack-induced electrical resistivity changes in cracked CNT-reinforced composites

Carbon nanotube (CNT)-reinforced composites exhibit a piezoresistive behavior that permits their use as sensors in novel structural health monitoring (SHM) applications, by measuring the electrical resistivity change of the CNT modified laminate. However, the presence of cracks in such composite materials may not only compromise their structural integrity, but may as well alter their capability to act as reliable piezoresistive sensors. In this paper, we conduct a numerical study aimed at quantifying how the presence of cracks in reinforced polymer composites does influence their electrical conductivity and, consequently, their sensor performance. To this end, the electromechanical constitutive properties of the composite are determined by a mixed micromechanics approach that allows characterizing both the elastic properties and the strain-induced alterations in the overall electrical conductivity of the CNT-reinforced composite. The strain response of the cracked composite domain is accurately determined by means of a dual Boundary Element (BE) approach. Electrical conductivity in the cracked composite follows from its computed strain state at each point in the domain. Subsequently, the resulting non-homogeneous electrical conductivity problem is solved using a finite differences scheme that also accounts for semipermeable crack-face electrical boundary conditions. Several parametric studies are conducted to illustrate the influence of various crack geometries in the piezoresistive behavior of CNT-reinforced composites at varying CNTs concentrations.

Bending analysis of thick functionally graded piezoelectric rectangular plates using higher-order shear and normal deformable plate theory

In this paper, bending-stretching analysis of thick functionally graded piezoelectric rectangular plates is studied using the higher-order shear and normal deformable plate theory. On the basis of this theory, Legendre polynomials are used for approximating the components of displacement field. Also, the effects of both normal and shear deformations are encountered in the theory. The governing equations are derived using the principle of virtual work and variational approach. It is assumed that plate is made of piezoelectric materials with functionally graded distribution of material properties. Hence, exponential function is used to modify mechanical and electrical properties through the thickness of the plate. Finally, the effect of material properties, electrical boundary conditions and dimensions are investigated on the static response of plate. Also, it is shown that results of the presented model are close to the three dimensional elasticity solutions.

A semi-analytical mesh-free method for 3D free vibration analysis of bi-directional FGP circular structures subjected to temperature variation

In this present paper, a semi-analytical mesh-free method is employed for the three-dimensional free vibration analysis of a bi-directional functionally graded piezoelectric circular structure. The dependent variables have been expanded by Fourier series with respect to the circumferential direction and have been discretized through radial and axial directions based on the mesh-free shape function. The current approach has a distinct advantage. The nonlinear Green-Lagrange strain is employed as the relationship between strain and displacement fields to observe thermal impacts in stiffness matrices. Nevertheless, high order terms have been neglected at the final steps of equations driving. The material properties are assumed to vary continuously in both radial and axial directions simultaneously in accordance with a power law distribution. The convergence and validation studies are conducted by comparing our proposed solution with available published results to investigate the accuracy and efficiency of our approach. After the validation study, a parametric study is undertaken to investigate the temperature effects, different types of polarization, mechanical and electric boundary conditions and geometry parameters of structures on the natural frequencies of functionally graded piezoelectric circular structures.

Tomographic Approach for Universal Tactile Imaging With Electromechanically Coupled Conductors

In this paper, we propose a novel, low-cost, and universal tactile sensing technology for imaging pressure distribution using a tomographic approach with conductors. In particular, we focus on the fact that pressure is related to the contact resistance between two conductive objects. The sensor comprises driving and probing conductors, which are electromechanically coupled. The system solves an inverse problem for estimating electrical boundary conditions using the voltage sets from electrodes on the border of the probing conductor. The sensing system successfully estimates the pressure distribution, contact location (error rate: 5.68 ± 2.78%), and local pressure (error in the range 0.0269 -0.0509 N/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for a maximum pressure of 0.50 N/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). Finally, tactile imaging by sheet- and finger-type sensors are demonstrated as practical applications of the developed sensor.

Actively controllable topological phase transition in homogeneous piezoelectric rod system

By employing periodic electrical boundary conditions, an innovative method to generate actively tunable topologically protected interface mode in a “homogeneous” piezoelectric rod system is proposed. Made of homogeneous material and with uniform structure, each unit cell of the piezoelectric rod system consists of three sub-rods forming an A-B-A structure, where the two A sub-rods have the same geometry and electric boundary conditions. It is discovered that the switch of electrical boundary conditions from A-closed and B-open to A-open and B-closed will yield topological phase inversion, based on which topologically protected interface mode is realized. When capacitors CA and CB are connected to the electrodes of sub-rods A and B, respectively, a variety of physical phenomena is observed. On one hand, varying the capacitance in a certain path leads to topological phase transition. On the other hand, different variation paths of the capacitors give rise to different locations of topological phase transition points. This discovery allows the eigenfrequency of the topologically protected edge mode thus formed be actively controlled by appropriately varying the capacitance. The active topological protected interface mode may find wide engineering applications that require high sensitivity sensing, nondestructive testing, reinforcing energy harvesting, information processing, and others.

Aeroelastic Flutter Analysis of Thick Porous Plates in Supersonic Flow

The aeroelastic flutter analysis of thick porous plates surrounded with piezoelectric layers in supersonic flow is studied. In order to aeroelastic analysis of the thick porous-cellular plate, Reddy’s third-order shear deformation plate theory and first-order piston theory are used. Furthermore, the plate is composed of two face piezoelectric layers and three functionally graded porous distributions core. Applying the extended Hamilton’s principle and Maxwell’s equation, the governing equations of motion are obtained. The partial differential governing equations are transformed into a set of ordinary differential equations by applying Galerkin’s approach. The effects of porosity coefficient, porosity distributions, piezoelectric layers, geometric dimensions, electrical and mechanical boundary conditions on the flutter aerodynamic pressure and natural frequencies of porous-cellular plates are investigated.

Characteristic Mode Analysis of Composite Metallic–Dielectric Structures Using Impedance Boundary Condition

In this article, an approach combining the electric field integral equation (EFIE) and impedance boundary condition (IBC) is presented for the characteristic mode analysis (CMA) of composite metallic–dielectric structures. Different from published works, only the electric currents are used in this approach and the computed eigencurrents are in a similar form as those of purely metallic structures. To ensure completeness and orthogonality of the eigencurrents, symmetry of the IBC-EFIE operator has been carefully examined. For lossy structures, a new formulation is deduced for CMA. The presented IBC-EFIE formulation is able to handle a variety of problems, e.g., lossy metals, thin dielectrics, thin dielectric-coated conductors, and metasurfaces. Several numerical examples are provided for those problems, and full-wave CMA solutions are used to verify the IBC-EFIE formulation. It is shown that this method is fairly accurate while computationally efficient, which makes CMA a promising tool for large scale or complex composite structures.

Enhancement of modal birefringence in solid core Bragg fibers with high-index-contrast claddings

Abstract We present two types of highly birefringent solid core Bragg fibers (SCBFs) with high-index-contrast claddings by asymmetrically introducing low index parts (LIPs) into the solid core. The characteristics of their modal birefringence and confinement loss are numerically investigated by using a full-vector finite element method. The simulation results reveal that the modal birefringences in such highly birefringent SCBFs essentially depend not only on the difference in electric field boundary condition between the orthogonal-polarized modes, but also on the photonic bandgap effect. Both types of highly birefringent SCBFs have higher modal birefringence than those with low-index-contrast claddings, owing to the large refractive index (RI) modulation ranges of the LIPs. The modal birefringence of the fundamental mode at the targeted 1550 nm is strongly dependent on the size, RI and location of LIPs. Notably, the linear relationship between the modal birefringence and the RI of LIPs in the y-direction in a highly birefringent SCBF with four LIPs included can serve as a new sensing mechanism for the RI measurement of liquid analytes. We believe that the results would be beneficial to the design and application of highly birefringent SCBFs with high-index-contrast claddings.

A phase-field model for anisotropic brittle fracturing of piezoelectric ceramics

Piezoelectric ceramics are inherently brittle materials that show electromechanical coupling under electrical and mechanical stimuli. In the last decades piezoelectric materials have garnered significant attention due to their established applications as sensors and actuators. In this context the structural reliability of such materials under varied conditions is paramount. In the present work we propose a phase-field approach to model crack propagation in a coupled electromechanical setting. The proposed framework accounts for anisotropic crack propagation by employing appropriate structural tensors that enter the crack-surface-density function as additional arguments. Appropriate choices of degradation functions allow for the accommodation of varied electrical boundary conditions along cracks. Based on experimental results available in the literature, we employ a non-associative dissipative framework in which fracturing processes are driven by the mechanical part of the coupled electromechanical driving force alone. The modeling capabilities of the proposed framework are demonstrated by a set of numerical examples in two and three spatial dimensions.

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

The paper studies the existence of surface acoustic waves in half-infinite one-dimensional piezoelectric phononic crystals consisting of perfectly bonded layers, which are arranged so that the unit cell is symmetric, i.e., is invariant with respect to inversion about its midplane. An example is a bilayered structure with exterior layer being half thinner than the interior layers of the same material. The layers may be generally anisotropic. The maximum possible number of surface acoustoelectric waves referred to a fixed wave number and a given full stop band is established for different types of electric boundary conditions at the mechanically free or clamped surface. In particular, it is proved that the phononic crystal-vacuum interface can support two surface waves in any full stop band. The same statement holds true in the case of a metallized surface of the crystal. This number is greater than that in a purely elastic case. In the presence of crystallographic symmetry, which decouples the sagittally and horizontally polarized surface waves, their separate admissible numbers are obtained. It is shown that the propagation along the normal to the surface is a special case, where the maximum number of surface waves is less than that along oblique directions.

Free Vibration Analysis of Smart Laminated Functionally Graded CNT Reinforced Composite Plates via New Four-Variable Refined Plate Theory

This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell’s equation and Hamilton’s principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed.