Electromechanical Coupling Field Research Articles

Nonlinear combination resonance analysis of parametric-forced excitation for an axially moving piezoelectric rectangular thin plate in thermal- electromechanical coupling field

In this paper, the combination resonance of parametric-forced excitation characteristics for an axially moving rectangular piezoelectric plate under a thermal-electromechanical field is studied. Based on Kirchhoff-Love plate theory and Von Karman theory, the transverse vibration governing equations are derived from Hamilton's principle. The equations are discretized to ordinary differential equations by the Galerkin method. Then, the multiple scales method is applied to solve the system combination resonance equation, two different resonance states and corresponding amplitude-frequency response equations are obtained by eliminating the secular term, respectively. Additionally, the stability of the steady-state responses is analyzed by Lyapunov stability. Based on the numerical analysis, the influence of axial velocity, external voltage, central temperature difference, structural damping, and other parameters on nonlinear combination resonance response are investigated. The effect of parameter variation on period-doubling bifurcation and the chaotic motion of the system are also discussed by the system global bifurcation diagram.

Studies of a new-style resonator to control electro-mechanical coupling bandgap of a locally resonant piezoelectric/elastic phononic crystal double-layer nonlocal nanobeam

The paper proposed a model of a locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam with periodically attached “spring-mass” resonator and additional spring between upper and lower nanobeams, as well as horizontal spring between mass and foundation. Euler beam theory and nonlocal piezoelectricity theory are coupled and introduced to plane wave expansion (PWE) method to calculate the band structures of such a model with different parameters. Numerical results and further analysis demonstrate that all the bands of double-layer nanobeam can be divided into symmetric and antisymmetric ones. Adding additional and horizontal springs play a role in control the symmetric and antisymmetric bands respectively, which make wider band gaps be opened than corresponding single-layer nanobeam. Moreover, the change of parameters of electro-mechanical coupling fields and resonator can be applied to effectively control the starting frequencies and widths of band gaps, which can provide a theoretical basis for active control of vibration. Effects of geometric and non-dimensional nonlocal parameters on band gaps are also discussed. All the studies are expected to be applied to actively control vibration propagation in the field of nano electro-mechanical system (NEMS).

Analysis of piezoelectric problems using zonal free element method

Recently, the free element method(FREM), a novel strong-form method, is successfully used to solve thermal and mechanical problems. However, similar to some other strong-form methods, it is difficult to handle the geometric model with corner points. To overcome this weakness, the zonal free element method (ZFREM), which has strong adaptability to deal with complex geometry, is proposed by introducing the sub-domain mapping technique. Besides, the proposed method is firstly applied to solve piezoelectric problems. A unified formulation for piezoelectric problems in the case of electro-mechanical coupling field is established by the zonal free element method. Several two-dimensional (2D) and three-dimensional (3D) examples are carried out and the results are compared with available analytical solutions and finite element solutions to demonstrate validity and accuracy of the proposed method.

Numerical simulation of electromechanical coupling properties of three-dimensional braiding piezoelectric composite actuator

In this paper, an innovative three-dimensional braiding piezoelectric composite actuator (3D-BPCA) is proposed. Based on the 3D braiding technology, the geometric model and representative volume unit (RVU) model of the 3D-BPCA are established. The effective elastic constant, dielectric constant and piezoelectric constant of the braiding piezoelectric composite layer (BPCL) are predicted. The electromechanical properties of the 3D-BPCA under the electromechanical coupling field is theoretically analyzed and numerically simulated, and compared with the piezoelectric ceramics actuator (PZT-5A). Numerical results show that the 3D-BPCA has better actuating properties than the PZT-5A and has a wide application prospects.

Finite element analysis of the three-dimensional crack and defects in piezoelectric materials under the electro-mechanical coupling field

This paper presents three-dimensional planar crack and non-planar defects analysis of piezoelectric materials by the finite element method (FEM). Based on practical engineering, a series of reasonable three-dimensional defects models are established. Different from the usual two-dimensional plane as a three-dimensional defect form, the present paper takes into account the different causes, concrete position, and various shapes of typically three-dimensional non-planar defects in practical engineering. By changing the geometric size of the defect and the electro-mechanical boundary conditions, the effects of three-dimensional defect geometry and different electro-mechanical coupling boundary conditions on the distribution of stress, electric field strength, and electric displacement around the defect are investigated. The calculation results show that the electro-mechanical parameters are strongly affected by the geometry of defect and boundary conditions. Furthermore, the distribution of electro-mechanical parameters in the detailed position of the different three-dimensional defect model is also studied, which can accurately assess the location where the defect is prone to fracture. It is concluded that this paper can be used as a reference of three-dimensional defects and the service life of piezoelectric materials in practical engineering structures.

Coupled nonlinear mechanics for the electromechanical response of multi-stable piezoelectric shallow shells with piezoelectric films

This paper considers the nonlinear electromechanical response of shallow piezoelectric laminated shells of arbitrary double curvature, undergoing to snap through buckling and eventually to elastic instability, under mechanical pressure loads. The computational framework is based on coupled nonlinear mechanics encompassing the electromechanical coupling field and geometric nonlinearity due to large displacements and rotations. The first shear deformation theory is combined with a linear layerwise theory for describing the elastic and electric state variables through the laminate thickness, respectively. The governing equations are expressed with respect to an orthogonal curvilinear coordinate system. Building upon the nonlinear multifield mechanics an eight-node shell finite element is developed to discretize the generalized coupled nonlinear equations, which are subsequently linearized and iteratively solved, using the Cylindrical Arc-Length method in combination with the Newton-Raphson iterative technique. Numerical results demonstrate the capability of the present model to predict the complex electromechanical response of shallow cylindrical shells that transit between two stable equilibrium states. The electromechanical (generated electric charge-energy) conversion is highly complex (depending on both nonlinear piezoelectric and stiffness matrices) and predicted along the stable and unstable paths of bi-stability. At the same time the feasibility to relate the sensory electric potential with the snap through buckling of smart shells is also quantified. The influence of shell thickness, curvature and laminate configuration on the electromechanical conversion, is finally investigated.

Full-wave modeling of micro-acoustofluidic devices driven by standing surface acoustic waves for microparticle acoustophoresis

Surface acoustic wave (SAW)-based acoustofluidic systems are emerging as an important tool for acoustophoresis. In this paper, we present a full cross-sectional model of standing SAW acoustofluidic devices for obtaining full-wave results. Our model involves a piezoelectric substrate with interdigitated electrodes and a rectangular water channel enclosed in a finite soft elastic solid. This model accounts for piezoelectric SAWs with electromechanical coupling, simultaneous transverse and longitudinal wave fields in the elastic solid from SAW radiation, and acoustic and streaming fields in the enclosed water channel in an integrated system by solving the elastodynamic and Navier–Stokes field equations. Accordingly, the acoustic radiation force and streaming-induced Stokes drag force are obtained to analyze the acoustophoretic motion of microparticles of different sizes. Using the full-wave results, we reveal the influences of the channel wall displacements and acoustic and flow fields in the water domain. The full-wave field also allows us to determine the effects of the channel dimensions and its location in the finite elastic solid on the force strengths. We demonstrate that the critical diameter of the microparticles can be reduced by an order of magnitude by changing the channel location, while maintaining the same acoustic frequency. We note that the results, mechanisms, and method presented in this study can be usefully applied to the rational design of standing SAW acoustofluidic devices and for developing innovative acoustophoretic systems involving complex structure–fluid interactions.

Electro-mechanical coupling band gaps of a piezoelectric phononic crystal Timoshenko nanobeam with surface effects

Plane wave expansion (PWE) method is extended to calculate the band structures of a proposed piezoelectric phononic crystal (PC) nanobeam by applying surface elasticity and Timoshenko beam theories. The calculation method is derived and formulized in detail. Further, electrical voltage and external axial force are picked to study the effects of electro-mechanical coupling fields on band gaps, residual surface stress and material intrinsic length are chosen to research the influences of surface effects on band gaps, and ratio between lengths of PZT-4 and epoxy in a unit cell and height-width ratio are picked to investigate the effects of geometric parameters on band gaps. In addition, all the results are compared to those in Euler nanobeam with same parameters. All the results and further analysis demonstrate that the influence rules will play an active role in design process and active control of nano electro-mechanical system based on piezoelectric PC nanobeam.

Singularity of Electromechanical Coupling Field in Piezoelectric Composite Junctions

The double singularities including singular stress field and singular electric displacement field, in the tips of piezoelectric composite junctions, are analyzed by the interpolation matrix method (IMM). The double singularity analysis problem of piezoelectric composite junctions is converted into eigenvalue solution problem of ordinary differential equations with variable coefficients under corresponding boundary conditions. In numerical examples, the first couple of singularity orders and the corresponding characteristic angular functions of displacement and electric potential for the electromechanical coupling field are obtained and comparisons are presented to validate the accuracy of the proposed method. The singularity of the electromechanical coupling field at the tip of piezoelectric composite material junctions is closely related to the bonding angle and fiber direction. According to the numerical results, the best scheme can be configured for the combination of dissimilar materials.

Numerical Modelling of Vibration Characteristics of a Partially Metallized Micro Electromechanical System Resonator Disc

In this paper, we report an extension of a polynomial and numerical vibrational characterization of an annular piezoelectric disc resonator partially covered with electrodes. The three governing partial differential equations of motion are solved to provide the frequency response of the piezoelectric disc using a polynomial approach. This method makes use of Legendre polynomials series to express the mechanical displacement components and the electrical potential which are introduced into the equations of motion of the piezoelectric structure. The principal advantage of this method consists of incorporating the electrical source, the boundary and continuity conditions directly into the governing equations by the use of position-dependent physical constants and by a wise choice of the polynomial expansions for the independent variables, the mechanical displacement components and the electrical potential. Both harmonic and modal analyses were studied and are presented. Numerical calculations based on the foregoing method were performed to present resonance and anti-resonance frequencies, electromechanical coupling coefficient, field profiles and electrical input admittance for PIC151 and PZT5A disc resonators with various metallization rates. The high accuracy and reliability of our approach is confirmed via a comparison of our results with their counterparts reported in literature.

Anisotropic mechanical behavior of gadolinia-doped ceria solid electrolytes under electromechanical coupling field using atomistic simulations

Gadolinia-doped ceria (GDC) is one of widely used electrolyte materials for solid oxide fuel cells (SOFCs) due to its high ionic conductivity. In this paper, we report the anisotropic mechanical behavior of GDC solid electrolytes under electromechanical coupling loading by molecular dynamics (MD) simulation. For pure CeO2, it is found that low electric field merely reduces the fracture strength while high electric field directly changes phase transformation behavior in the [100] and [110] crystal orientations. In the [111] crystal orientation, the increase of electric field lead to the synchronous elevation of fracture stress by weakening the electrostatic repulsion between adjacent oxygen ions. And the doping concentration and temperature are considered to investigate the fracture behavior with electric field loading. Moreover, significant improvement of electrolyte conductivity is obtained by loading electric field on GDC. This finding might be able to provide a reasonable insight to reduce operating temperature of SOFC system.

Nonlinear bandgap properties in a nonlocal piezoelectric phononic crystal nanobeam

Applying nonlocal elasticity theory, von Kármán type nonlinear strain-displacement relation and plane wave expansion (PWE) method to Euler-Bernoulli beam, the calculation method of band structure of a nonlinear nonlocal piezoelectric phononic crystal (PC) nanobeam is proposed and formulized. In order to investigate the properties of wave propagating in the nanobeam in detail, band gaps of first four orders are picked, and the corresponding influence rules of electro-mechanical coupling fields, nonlocal effect and geometric parameters on band gaps are studied. During the researches, external electrical voltage and axial force are chosen as the influencing parameters related to electro-mechanical coupling fields. Scale coefficient is chosen as the influencing parameter corresponding to nonlocal effect. Length ratio between materials PZT-4 and epoxy and height-width ratio are chosen as the influencing parameters of geometric parameters. Moreover, all the influence rules are compared to those in linear nanobeam. The results are expected to be of help for the design of micro and nano devices based on piezoelectric periodic nanobeam.

An accurate and efficient method for the piezoelectric coated functional devices based on the three-dimensional Green's functions under a tangential point force

An accurate and efficient method for the electro-mechanical coupling fields of piezoelectric coated structure is presented in this paper. First, the three-dimensional Green's function for a tangential point force on the surface of coated structure combined with orthotropic piezoelectric coating and orthotropic elastic substrate is presented in the form of elementary functions based on the general solution method. Then, the corresponding electro-mechanical coupling fields of this coated structure under arbitrary mechanical loads can be obtained by superposition principle and Gauss integration. At last, numerical simulations are given to show the usage of this method in the analyses of interface effect, interface debonding and tensile failure. And this method may suggest possible mechanisms by which layered structures can be designed for engineering applications.

Study on the interactions between the coatings of electric conductor or dielectric media and piezoelectric substrate in the piezoelectric functional devices

Because that most of piezoelectric functional devices are combined with the coatings of electric conductor or dielectric media and the piezoelectric substrate, the study on the interactions between them is valuable for their advanced design. In this paper, a method for the electro-mechanical coupling fields in these piezoelectric functional devices is presented. Firstly, the two-dimensional Green’s function for a normal line force or line charge is derived. Then, based on the obtained Green’s function, the interaction mechanism between the coatings of electric conductor or dielectric media and the piezoelectric substrate is studied. Finally, the electro-mechanical coupling fields under arbitrary loads are obtained by superposition principle and Gauss integration. Numerical results show that this method has high computational precision, efficiency and stability. And it can be used to improve the reliability and working performance of the piezoelectric functional device effectively.

An accurate and efficient method for piezoelectric coated functional devices based on the two-dimensional Green’s function for a normal line force and line charge

Because most piezoelectric functional devices, including sensors, actuators and energy harvesters, are in the form of a piezoelectric coated structure, it is valuable to present an accurate and efficient method for obtaining the electro-mechanical coupling fields of this coated structure under mechanical and electrical loads. With this aim, the two-dimensional Green’s function for a normal line force and line charge on the surface of coated structure, which is a combination of an orthotropic piezoelectric coating and orthotropic elastic substrate, is presented in the form of elementary functions based on the general solution method. The corresponding electro-mechanical coupling fields of this coated structure under arbitrary mechanical and electrical loads can then be obtained by the superposition principle and Gauss integration. Numerical results show that the presented method has high computational precision, efficiency and stability. It can be used to design the best coating thickness in functional devices, improve the sensitivity of sensors, and improve the efficiency of actuators and energy harvesters. This method could be an efficient tool for engineers in engineering applications.

Polynomial approach for modeling a piezoelectric disc resonator partially covered with electrodes

The frequency spectrum of a partially metallized piezoelectric disc resonator was studied using Legendre polynomials. The formulation, based on three-dimensional equations of linear elasticity, takes into account the high contrast between the electroded and non-electroded regions. The mechanical displacement components and the electrical potential were expanded in a double series of orthonormal functions and were introduced into the equations governing wave propagation in piezoelectric media. The boundary and continuity conditions were automatically incorporated into the equations of motion by assuming position-dependent physical material constants or delta-functions. The incorporation of electrical sources is illustrated. Structure symmetry was used to reduce the number of unknowns. The vibration characteristics of the piezoelectric discs were analyzed using a three-dimensional modelling approach with modal and harmonic analyses. The numerical results are presented as resonance and anti-resonance frequencies, electric input admittance, electromechanical coupling coefficient and field profiles of fully and partially metallized PIC151 and PZT5A resonator discs. In order to validate our model, the results obtained were compared with those published previously and those obtained using an analytical approach.

Theoretical analysis on shear-bending deflection of a ring-shape piezoelectric plate

In this paper, the electromechanical coupling field in shear-bending mode for a ring-shape piezoelectric plate was theoretically established. According to the classical small bending elastic plate theory and piezoelectric constitutive equations, the analytical solution to the bending deformation of the piezo-actuator under electric field and a concentrated or uniformly distributed mechanical load was achieved. The mechanism for generating bending deformation is attributed to axisymmetric shear strain, which further induces the bending deformation of the single ring-shape piezoelectric plate. This mechanism is significant different from that of piezoelectric bimorph or unimorph actuators reported before. Our analysis offers guidance for the optimum design of a ring-shape shear-bending piezo-actuator.

Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes

The Legendre polynomial method has been extended to the modeling of MEMS resonator disc partially covered with electrodes. The disc has been divided into two areas: one with electrodes and the other without electrodes. For each area, The Maxwell equations and the piezoelectric constitutive equations of motion are studied and solved to yield a frequency response and electrical behavior of the MEMS resonator applying a semi analytical method based on a Legendre polynomials series and trigonometric functions. However, the method allows incorporating the boundary conditions directly into the governing equations by assuming position-dependent of elastic constants, mass density and delta functions. The alternating electrical source is described by specific terms which are also introduced into the equation of motion. The formalism has been developed which allows for both harmonic and modal analyses. In order to validate our polynomial approach, numerical results are presented such as resonant and anti-resonant frequencies, electric input admittance, electromechanical coupling coefficient and field profiles of fully and partially metallized PZT5A resonator discs. The results obtained were compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the contour modes of all orders.

Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity

Due to large surface to volume ratio and manifest strain gradients typically present in nanostructures, it is essential to incorporate both surface effects and flexoelectricity in studying the size-dependent electromechanical coupling behaviors of piezoelectric materials at the nano-scale. In the current work, a modified Kirchhoff plate model with the consideration of residual surface stress, surface elasticity, surface piezoelectricity, and flexoelectricity is developed to investigate the electroelastic responses and vibrational behaviors of a bending piezoelectric nanoplate (PNP). The governing equations and the corresponding boundary conditions accounting for both the surface effects and the flexoelectricity are derived by the variational principle. Ritz approximate solutions of the static bending and the free vibration indicate that these nano-scale features are more prominent for thinner plates with smaller thickness. The simulation results also reveal that the influence of the flexoelectricity and the surface effects upon the bending behaviors of the PNP depends on the applied electrical loading and the plate dimensions. Moreover, it is also observed that the frequency tuning of PNP-based nanoresonators by adjusting applied electrical load can be modified by both the flexoelectricity and the surface effects. The current work is expected to provide increased understanding on the theoretical basis for the design and applications of PNP-based nanodevices.

Evaluation of Fatigue of the Lead Zirconate Titanate Ceramics under Electro-mechanical Coupling Field

Modified small punch (MSP) tests are effective evaluation methods for mechanical properties by using small specimens. Fatigue properties of PZT ceramics under electro-mechanical coupling field and pure force field were evaluated with multi-fields coupling MSP tests. It is found that the fracture strength of the samples under electro- mechanical field would sharply decrease, compared with the samples under pure force field. Fatigue life would de- crease greatly and intergranular fracture would happen easily under electro-mechanical coupling field.