Electric Potential Function Research Articles

Ferroionic states in ferroelectric thin films

The electric coupling between surface ions and bulk ferroelectricity gives rise to a continuum of mixed states in ferroelectric thin films, exquisitely sensitive to temperature and external factors, such as applied voltage and oxygen pressure. Here we develop the comprehensive analytical description of these coupled ferroelectric and ionic ("ferroionic") states by combining the Ginzburg-Landau-Devonshire description of the ferroelectric properties of the film with Langmuir adsorption model for the electrochemical reaction at the film surface. We explore the thermodynamic and kinetic characteristics of the ferroionic states as a function of temperature, film thickness, and external electric potential. These studies provide a new insight into mesoscopic properties of ferroelectric thin films, whose surface is exposed to chemical environment as screening charges supplier.

An efficient multiscale computational formulation for geometric nonlinear analysis of heterogeneous piezoelectric composite

In this contribution, an efficient multiscale computational formulation is developed for the geometric nonlinear analysis of heterogeneous piezoelectric materials. In this formulation, the relations between the microscopic heterogeneous properties and macroscopic behaviors of the piezoelectric composite are established by the numerically constructed displacement and electric potential base functions. The heterogeneous and complex microstructure can be equivalent to a simple macroscopic piezoelectric coarse element through those constructed multiscale base functions. Then the equivalent tangent stiffness matrix and internal force vector of the macroscopic coarse element are deduced based on the co-rotational approach, which can describe the motion of macroscopic coarse element clearly and efficiently. Thus the original electro-mechanical coupling geometric nonlinear problem could be solved iteratively on the macroscopic scale, which will save a tremendous amount of computing time and cost. After all the macroscopic calculations, the microscopic mechanical and electrical responses could be retrieved and calculated from the macroscopic solutions by using the above-mentioned multiscale shape functions. To verify the validation and high-efficiency of the proposed multiscale computation formulation, several typical numerical examples are carried out. All the computation results indicate that the developed multiscale formulation not only could provide high precision solutions but also has high efficiency.

The Rotation Effect on Shear Horizontal Surface Wave in a Piezoelectric Semi-Space Covered by a Semiconductor Film

In this study, a mathematical model of the rotation effect on Shear Horizontally wave (SH-wave) propagation in a piezoelectric semi-space covered by a semiconductor film is investigated. The semiconducting layer is rotating with a constant angular velocity and the interface between the piezoelectric substrate and the semiconductor layer is imperfectly bonded. Furthermore, the surfaces of the bilayer system assumed free of traction and electrically shorted or open. The governing equations of the dynamical displacement and electrical potential function under the effect of rotation are driven by solving the coupled electromechanical field equations of the piezoelectric half-space and the semiconductor film. In addition, the exact frequency equations of SH waves are derived. Next, the numerical examples are considered to clarify the effects of rotation and electromagnetic boundary conditions for the different values of the film thickness and wave number on the dispersion behaviors. Finally, the effect of rotation on the frequency equation is investigated in detail for piezoelectric material PZT-5H and the semiconductor silicon. The obtained results provide a predictable and theoretical basis for applications of piezoelectric and semiconductor structures to surface acoustic wave equipments.

Analysis of electric current density in carbon fiber reinforced plastic laminated plates with angled plies

It is important to know the electric current distribution in a laminated carbon fiber reinforced plastics (CFRP) plates for safety analysis of lightning strikes and for damage monitoring of plates based on changes in electrical resistance. An orthotropic electric potential function has been previously proposed, which was effective for modeling of a CFRP cross-ply laminate used in beam structures. However, that method is limited to cross-ply laminates that contain no angle plies, while CFRP plate structures typically feature angle plies. In the present study, a new analysis method is proposed for laminated CFRP plates that contain angled plies. In the new method, two or three angle plies are coupled and assumed to have orthotropic conductivity of double or triple thickness. A new method to calculate the equivalent conductivity is also proposed. The new method is applied to two types of laminates containing angle ply structures. The results obtained are compared with those from a finite difference method and from experimental measurements. The new method is shown to be effective for analysis of the electric current of laminates that contain angled plies.

Crack swarm inspection for estimation of crack location in carbon fiber reinforced plastics: A numerical study

The present study proposes crack swarm inspection (CSI) for estimating crack location and size in carbon composite laminates from the surface voltage distribution. This technique generates a large number of virtual microscopic cracks, and calculates the surface voltage distribution of the composites using anisotropic electric potential functions and doublet strings. Using genetic algorithms, the virtual microscopic cracks formed a swarm to coincide with the measured surface voltage; thereby, the crack sizes and locations are estimated from the position of the crack swarm. The CSI was applied to crack detection in carbon laminated composite plates; it was confirmed that the existence of cracks in each partitioned section was detected with >80% probability, in reference to the crack location and size information. Furthermore, we also confirmed that the estimation accuracy was affected by the electric current density in the thickness direction, and addressed the recommended electrode interval based on the minimum size of the estimated crack.

The Frequency Equations for Shear Horizontal Waves in Semiconductor/Piezoelectric Structures Under the Influence of Initial Stress

In this paper, we investigated analytically the frequency equations for shear horizontal wave propagation in a piezoelectric half space covered by a semiconductor film with initial stress effect. The semiconducting layer is influenced by initial stress and the interface between the piezoelectric substrate and the semiconductor layer. The governing equations of the mechanical displacement and electrical potential function under the effect of initial stress are obtained by solving the coupled electromechanical field equations of the piezoelectric half-space and the semiconductor film. Next, the numerical examples are presented to illustrate the influence of initial stress and electromagnetic boundary conditions for the different values of the film thickness and wave number. Furthermore, we studied in more details the effect of initial stress on the frequency equation for piezoelectric Barium Titanate (BaTiO3) and semiconductor silicon. The obtained results provide a predictable and theoretical basis for applications of piezoelectric and semiconductor composites to acoustic wave devices.

A design of active constrained layer damping treatment for vibration control of circular cylindrical shell structure

A new 1-3 viscoelastic composite material (VECM) layer is designed for improved active constrained layer damping (ACLD) treatment of vibration of a functionally graded (FG) circular cylindrical shell. Besides this improved active damping treatment, another objective of this study is to control all the modes of vibration of the shell effectively using the treatment (active constrained layer damping) in layer-form throughout the outer shell-surface. In this design of active constrained layer damping treatment in layer-form, its (active constrained layer damping) necessary conformability with the curved host shell-surface is ensured by the use of a vertically reinforced 1-3 piezoelectric composite (PZC) constraining layer, whereas the effective control of several modes of vibration of the shell is achieved by the use of electrode-patches over the surfaces of the constraining layer. A fruitful strategy in the arrangement of electrode-patches is proposed for effective control of several modes of vibration of the shell using one configuration of the electrode-patches. An electric potential function is assumed for this use of electrode-patches and a geometrically nonlinear coupled electro-visco-elastic incremental finite element model of the overall shell is developed for its analysis in the frequency-domain. The analysis reveals significant improvement of active damping characteristics of the active constrained layer damping layer for the use of the present 1-3 viscoelastic composite material layer instead of the traditional monolithic viscoelastic material (VEM) layer. The analysis also reveals the suitability of the present strategy of arrangement of electrode-patches for achieving aforesaid control-activity of the ACLD layer. The effects of temperature in the host functionally graded shell and different geometric parameters in the design of the 1-3 viscoelastic composite material layer on the damping characteristics of overall shell are also presented.

In Vitro Biocompatibility of Si Alloyed Multi-Principal Element Carbide Coatings.

In the current study, we have examined the possibility to improve the biocompatibility of the (TiZrNbTaHf)C through replacement of either Ti or Ta by Si. The coatings were deposited on Si and 316L stainless steel substrates by magnetron sputtering in an Ar+CH4 mixed atmosphere and were examined for elemental composition, chemical bonds, surface topography, surface electrical charge and biocompatible characteristics. The net surface charge was evaluated at nano and macroscopic scale by measuring the electrical potential and work function, respectively. The biocompatible tests comprised determination of cell viability and cell attachment to the coated surface. The deposited coatings had C/(metal+Si) ratios close to unity, while a mixture of metallic carbide, free-carbon and oxidized species formed on the film surface. The coatings’ surfaces were smooth and no influence of surface roughness on electrical charge or biocompatibility was found. The biocompatible characteristics correlated well with the electrical potential/work function, suggesting a significant role of surface charge in improving biocompatibility, particularly cell attachment to coating's surface. Replacement of either Ti or Ta by Si in the (TiZrNbTaHf)C coating led to an enhanced surface electrical charge, as well as to superior biocompatible properties, with best results for the (TiZrNbSiHf)C coating.

Performance of a short piezoelectric fiber–reinforced composite actuator in vibration control of functionally graded circular cylindrical shell

For improved flexibility and conformability of piezoelectric fiber–reinforced composite actuator, it is reconstructed in a recent study by the use of short piezoelectric fibers (short piezoelectric fiber–reinforced composite) instead of continuous fibers (continuous piezoelectric fiber–reinforced composite). This modification facilitates its application in short piezoelectric fiber–reinforced composite layer form instead of continuous piezoelectric fiber–reinforced composite patch form particularly in case of host structures with highly curved boundary surfaces. But the corresponding change in actuation capability is a major issue for potential application of short piezoelectric fiber–reinforced composite that is studied in this work through the control of vibration of a functionally graded circular cylindrical shell under thermal environment. First, an arrangement of continuous piezoelectric fiber–reinforced composite actuator patches over the host shell surface is presented with an objective of controlling all modes of vibration. Next, the use of short piezoelectric fiber–reinforced composite actuator layer for similar control activity is demonstrated through an arrangement of electrode patches over its surfaces. Subsequently, an electric potential function is assumed for the consideration of electrode patches and a geometrically nonlinear coupled thermo-electro-mechanical incremental finite element model of the harmonically excited overall functionally graded shell is developed. The numerical results reveal actuation capability of short piezoelectric fiber–reinforced composite actuator layer with reference to that of the existing continuous piezoelectric fiber–reinforced composite/monolithic piezoelectric actuator patches. The effects of temperature, size of electrode patches, properties of piezoelectric fiber–reinforced composite, and functionally graded properties on the control activity of short piezoelectric fiber–reinforced composite/continuous piezoelectric fiber–reinforced composite actuator are also presented.

Nonlinear resonant frequency of graphene/elastic/piezoelectric laminated films under active electric loading

This paper reports a result of investigation on the nonlinear resonant characteristics of graphene/elastic/piezoelectric (GEP) asymmetric laminated films under exciting electric loading, based on nonlocal elastic theory and von Karman strain–displacement relations in an active control system. The nonlinear dynamic governing equations containing deflection function, stress function and electric potential function are firstly constructed by Hamilton's principle, then are solved by the iterative homotopy harmonic balance method. Results show that the nonlinear resonant frequency of GEP laminated films can be controlled by adjusting the voltage exerted on piezoelectric layer according to engineering requirement, and the material property of elastic layer has a significant effect on the nonlinear resonant frequency of GEP laminated films, where the nonlinear behavior of resonant frequencies increases as the ratio of vibration amplitude to thickness of laminated films increases.

Influence of vibrations and rotations of diatomic molecules on their physical properties: I. Dipole moment and static dipole polarizability

Electronic dipole moment and static polarizability functions for some diatomic molecules (H2, N2, O2, NO, OH, CO, CH, HF and HCl) that are important for combustion and atmospheric chemistry are calculated by using ab initio methods over a broad range of internuclear distances. Using the ab initio calculated data on the electric properties and potential energy functions, the effective values of dipole moment and static polarizability as well as the energy levels of these molecules in individual vibrational and rotational states until the dissociation threshold are determined. It is revealed that, for the ground electronic states of molecules under study, the excitation of molecule vibrations can affect the averaged dipole moment and static polarizability substantially, whereas the effect of excitation of the rotational states is less pronounced.

Electric potential function of oblique current in laminated carbon fiber reinforced polymer composite beam

Orthotropic electric potential function analysis has shown to be applicable to the calculation of electric current density in laminated carbon composites. In our previous study, the analysis was limited to cases in which the electric current flows near the surface of the laminate. In some cases, the electric current flows in the through-thickness direction. When electric current flows in the thickness direction, the electric potential difference is completely different from that observed in the previous case. This study presents the new development of oblique flow potential analysis. The results of the analysis are verified by comparison with the results of FEM analysis and experimental measurements. Beam-type specimens containing two stacking sequences are used. The results indicate that the use of equivalent conductivity is effective for oblique electric flow. The experimental results show that the carbon fiber reinforced composites can be treated as a homogeneous material even for oblique electric current.

Electroelastic response of a piezoelectric cylinder with D∞ symmetry under axisymmetric mechanical loading

To understand the electroelastic field in fibers made of biodegradable polymers such as poly-l-lactic acid, we theoretically analyze the axisymmetric electroelastic field in a solid and infinitely long cylinder with D∞ symmetry, when subjected to a combined pressure and torsional shear stress. By introducing two kinds of displacement potential functions and an electric potential function and applying a Fourier transform technique, we derive the formulae for the electroelastic field quantities inside the body. Moreover, by performing numerical calculations, we elucidate the field both qualitatively and quantitatively, and investigate the possibility of using fibers made of poly-l-lactic acid for medical engineering applications.

Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton\'s principle and Maxwell\'s equation. The Navier\'s type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio (hp/2h), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.

Electric current distribution of carbon fiber reinforced polymer beam: analysis and experimental measurements

The authors have previously proposed an effective method for analyzing the electric current density of carbon fiber-reinforced polymer (CFRP) composites using an anisotropic electric potential function. The method is based on the assumption that CFRP laminates are homogeneous orthotropic materials. Actual CFRP laminates are, however, heterogeneous materials, having resin-rich layers and carbon fiber layers. In the present study, the electric conductance is calculated on the assumption that CFRP laminates are homogeneous using electrical resistance data measured by a four-probe method, and used for electric current analysis. A new specimen design is proposed to allow the electric current distribution of CFRP laminates to be investigated experimentally. The results obtained confirm that our analysis method is accurate for determining the electric current density of actual CFRP laminates. Thus, the assumption that CFRP laminates may be considered homogeneous orthotropic materials for electric current analysis is experimentally verified.

Nonlinear frequency shift behavior of graphene–elastic–piezoelectric laminated films as a nano-mass detector

• Nonlinear frequency shift of graphene–elastic–piezoelectric laminated mass detectors. • Adjusting voltage applied on the piezoelectric layer in mass detector can enhance its sensitivity. • Frequency shift at the center of GEP laminated mass detectors presents maximum. • The small scale effect decreases the effect of attached mass on the frequency shift. This paper presents an analytical method to investigate the nonlinear frequency shift of graphene–elastic–piezoelectric (GEP) laminated films as a resonant mass detector. Based on the nonlocal elastic theory and nonlinear geometrical relation, the nonlinear dynamic governing equations containing deflection function, stress function and electric potential function are constructed by Hamilton's principles, then are solved by Galerkin method and the iterative homotopy harmonic balance method. The effects of some key parameters on the nonlinear frequency shift are described. Results show that both nonlinearity and nonlocal parameter appear in significant influences on the frequency shift of GEP laminated nano-mass detector, and the frequency shift can be controlled by adjusting the external voltage acted on the piezoelectric layer when different mass particles attach to the detector surface. The present work can serve as a guideline for the design of a nanoscale resonant mass detector or other GEP-films based electromechanical resonator sensors.

A general solution technique for electroelastic fields in piezoelectric bodies with D ∞ symmetry in cylindrical coordinates

To elucidate the electroelastic field in bodies with D ∞ symmetry such as wooden materials, we constructed a general solution technique for electroelastic problems in such bodies in a cylindrical coordinate system. We introduced the displacement and electric potential functions to express the displacement and electric field in cylindrical coordinates; their governing equations were obtained using the fundamental equations for the electroelastic field. The electroelastic field quantities could be expressed in terms of two elastic displacement potential functions and two piezoelastic displacement potential functions, each of which satisfies a Laplace equation with respect to the appropriately transformed cylindrical coordinates. As an application of the technique, we analyzed the problem of an infinitely long cylinder subjected to a non-axisymmetrically distributed electric surface potential. Using numerical calculations, we elucidated the electroelastic field quantities within the cylinder and found unique electroelastic coupling behaviors, which clearly demonstrate the necessity for the analytical technique presented. Moreover, we confirmed the possibility of the nondestructive evaluation (NDE) techniques by use of the piezoelectric effects.

Subsonic Flow for the Multidimensional Euler–Poisson System

We establish the existence and stability of subsonic potential flow for the steady Euler–Poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on a non-insulated boundary from a fixed point at the exit, and prescribing the pressure at the exit of the nozzle. The Euler–Poisson system for subsonic potential flow can be reduced to a nonlinear elliptic system of second order. In this paper, we develop a technique to achieve a priori $${C^{1,\alpha}}$$ estimates of solutions to a quasi-linear second order elliptic system with mixed boundary conditions in a multidimensional domain enclosed by a Lipschitz continuous boundary. In particular, we discovered a special structure of the Euler–Poisson system which enables us to obtain $${C^{1,\alpha}}$$ estimates of the velocity potential and the electric potential functions, and this leads us to establish structural stability of subsonic flows for the Euler–Poisson system under perturbations of various data.

The statistical characteristics of protein hydration shells: A computer simulation

Water molecules and the hydrogen-bond network are essential structural components of many biological macromolecular systems, such as nucleic acids, as well as fibrillar and globular proteins. The water density in the protein hydration shell is known to differ from that of bulk water. In this paper, spatial density as function of the distance from the protein surface is discussed. The electric potential function is considered in the same way. The resulting profiles of the bound water density are characterized by the presence of several distinct maxima due to the existence of the regular structure of bound water at distances over 7 A. The minor discrepancies that are observed in both radial functions for different proteins are explained by topological variations that were revealed earlier by studying the valence and dihedral angle-distribution functions for water bound to the same proteins.

Generalized Bleustein-Gulyaev type waves in layered porous piezoceramic structure

The propagation of a Bleustein-Gulyaev (B-G) type wave in a structure consisting of multiple layers and a half-space of porous piezoelectric materials is theoretically studied. The solutions of the problem in terms of the mechanical displacements and electric potential functions are obtained for each layer and the half-space. The dispersion equation is obtained for electrically open and shorted boundary conditions by use of the transfer matrix method. A peculiar kind of B-G waves is investigated, which can propagate only in the layer over the half-space. The relationship between the piezoelectric constants and the dielectric constants is found for the existence of a peculiar kind of propagation modes. The numerical results in terms of the phase velocity and the electromechanical coupling factor with different thicknesses of the layer stack are presented.