Electrical Boundary Conditions Research Articles

A nonlinear analysis of electrically forced vibrations of piezoelectric plates with viscous damping near the thickness-shear mode

Based on the theory of nonlinear piezoelectricity, an approximate solution for electrically forced nonlinear thickness-shear vibrations of piezoelectric plates is introduced. The model considers an infinite piezoelectric plate subjected to an alternative voltage, incorporating 3rd-order and 4th-order elastic constants and viscous damping under finite deformation. The system's differential equations for steady-state forced vibrations are derived from the nonlinear pure thickness-shear vibration problem, and transformed so that the new electrical boundary conditions are free. After the application of Galerkin's method, the transformed differential equations lead to a cubic equation, capturing the nonlinear current-frequency curves of AT-cut quartz plates without the need of the quality factor Q, due to the introduced viscous damping. When the damping effect is ignored, the frequency response curves of the AT-cut quartz plate under a specific voltage are confirmed with the existing literature. The study emphasizes the presence of the critical voltage and the importance of the fourth-order elastic constant (c6666) in the stability, revealing lower c6666 values correspond to improved stability. Additionally, a proposed algorithm efficiently determines critical voltages for resonator stability.

Revealing the three-dimensional arrangement of polar topology in nanoparticles

In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.

Love wave propagation in a trigonal piezoelectric material layer of 32 crystal class

This paper analytically investigates the propagation characteristics of Love waves in a 32 trigonal piezoelectric layer resting on an elastic substrate. The governing electromechanical equations are derived and dispersion equations are obtained for two electrically open and short conditions. For a numerical study, a structure consisting of an α-quartz layer bonded onto a diamond substrate is considered. The influence of electrical boundary conditions on the mechanical and electrical responses is presented and discussed. The numerical results of dispersion curves indicate that phase velocities of all modes initiate at the shear wave velocity of the substrate and the phase velocity of the first mode approaches the velocity of the Bleustein–Gulyaev (BG) wave at high wavenumbers. Despite hexagonal piezoelectric material, the real and imaginary parts of the response mode shapes do not have identical distribution in a structure containing a piezoelectric material of crystal class 32. In addition, the present study provides a theoretical foundation for the design and application of surface acoustic wave (SAW) devices.

Локализованные акустические волны в одномерных периодически модулированных структурах

A number of one-dimensional phononic crystals, which are periodic thin-film structures of various geometries, consisting of sets of columns and metal inclusions located on a piezoelectric half-space, have been proposed and studied. The features of propagation in such structures of acoustic waves localized near the free surface and inhomogeneous inclusions have been studied. An unusual behavior of the dispersion curves for the studied localized modes was discovered. Particular attention is drawn to the so-called forbidden zones, i.e. frequency ranges in which there are no propagating localized modes. The influence of mechanical and electrical boundary conditions on the spectrum of the waves under study is discussed in detail.

Suppression of radial motion in translated field-reversed configuration plasma via global gyro-effect

Abstract The radial motion of a field-reversed configuration (FRC) during translation at supersonic/Alfvénic speed was effectively suppressed by the global gyro-effect induced by toroidal flow. In magnetohydrodynamic approximation, an FRC is inherently unstable against radial motions such as tilt and wobble. Surprisingly, the magnetic structure of the FRC remained intact even during translation at speeds exceeding the ion sonic and Alfvén speeds, despite the presence of radial motions. Optical observations were conducted on the radial motion and toroidal flow of translated FRCs under various electric boundary conditions at the device end. The implementation of end-shorting led to an increased toroidal flow rate, consequently reducing the radial displacement of the FRC during translation. This control of toroidal flow from the device’s end not only suppressed radial motion but also facilitated head-on collisions in the formation of FRCs by the collisional merging technique. The findings emphasize the significance of toroidal flow control in preserving the integrity of FRC’s simply connected geometry and enhancing its formation performance.

Macroscopic Polarization from Nonlinear Gradient Couplings.

We show that a lattice mode of arbitrary symmetry induces a well-defined macroscopic polarization at first order in the momentum and second order in the amplitude. We identify a symmetric flexoelectric-like contribution, which is sensitive to both the electrical and mechanical boundary conditions, and an antisymmetric Dzialoshinskii-Moriya-like term, which is unaffected by either. We develop the first-principles methodology to compute the relevant coupling tensors in an arbitrary crystal, which we illustrate with the example of the antiferrodistortive order parameter in SrTiO_{3}.

Free vibration of the piezoelectric laminated composite beams under the elastic foundation

Due to its self-adaptability and electric-mechanical interaction, the piezoelectric laminated composite structure has received increased attention in the engineering community, with the intricacy of the actual scenario, the structural stability based on numerous foundations has also been recognized. In this paper, a unified formulation which is based on classical laminated beam is presented to conduct free vibration analysis of piezoelectric laminated beams subjected to classical boundary conditions with the varied elastic foundations. The semi-analytical solutions of layered beams in various boundaries have been obtained based on the two-dimensional piezoelectric elastic theory and state space-differential quadrature method (SS-DQM), the solution of the general structural equation has been generated introducing the electrical boundary conditions and interlayer continuity conditions with this understanding. The different elastic foundations have been used to calculate the frequency equation of the piezoelectric laminated construction. The proposed finite element model is validated through the analysis of the piezoelectric laminated composite beam (PLCB) using the SS-DQM, and the present solutions are compared with those available in the literature to confirm their validity. A systematic parameter study for the piezoelectric laminated beams with various boundary conditions, piezoelectric parameters, lamina numbers and thickness ratios is also performed. The results of the PLCBs with various boundary constraints under the elastic foundation are presented and they may be served as a benchmark for researchers in this field.

Analytical assessment of wave dynamics for natural fibre-reinforced composite plates

This study presents a mathematical modelling to investigate the wave propagation behaviour in laminated natural fibre-reinforced composite plates integrated with surface bonded piezoelectric materials. To model wave dynamics, the constitutive relations, and governing equations of wave motion are derived based on different plate theories and Maxwell's electricity equation due to the surface bonded piezoelectric materials with the closed-circuit electrical boundary condition and transverse poling direction. The influence of natural fibres, as the reinforcing material of the host laminated composite plate, on wave propagation is studied and compared with the effects of synthetic fibres (i.e., carbon, Kevlar, and E-glass). The effects of other factors such as fibre volume fraction, laminate stacking sequence, and the presence of piezoelectric materials on wave dynamics are also investigated. The results of the wave propagation analysis reveal that the impact of different parameters on wave dynamics depends on the range of wavenumbers and wave mode numbers considered. It is found that some parameters may exhibit a noticeable influence on wave velocities, while others may have a negligible effect. The effect of piezoelectric materials on wave velocities in composite plates reinforced with natural fibres e.g., bamboo fibres, may differ from that observed in synthetic fibre-reinforced composite plates.

Numerical Stability of Dual Full-Wave Formulations With Electric Circuit Element Boundary Conditions

Numerical Stability of Dual Full-Wave Formulations With Electric Circuit Element Boundary Conditions

A 2D ferroelectric vortex pattern in twisted BaTiO3 freestanding layers

The wealth of complex polar topologies1–10 recently found in nanoscale ferroelectrics results from a delicate balance between the intrinsic tendency of the materials to develop a homogeneous polarization and the electric and mechanical boundary conditions imposed on them. Ferroelectric–dielectric interfaces are model systems in which polarization curling originates from open circuit-like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux-closure11–14 domains that evolve into vortex-like structures at the nanoscale15–17 level. Although ferroelectricity is known to couple strongly with strain (both homogeneous18 and inhomogeneous19,20), the effect of mechanical constraints21 on thin-film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles provides an opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated with the twisting. Furthermore, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding provides opportunities to create two-dimensional high-density vortex crystals that would enable us to explore previously unknown physical effects and functionalities.

Analysis of an interface crack with multiple electric boundary conditions on its faces in a one-dimensional hexagonal quasicrystal bimaterial

Analysis of an interface crack with multiple electric boundary conditions on its faces in a one-dimensional hexagonal quasicrystal bimaterial

Dual-functional perforated metamaterial plate for amplified energy harvesting of both acoustic and flexural waves

Metamaterials with defect states are commonly utilized in energy harvesting from acoustic and elastic waves due to their remarkable ability to localize waves. In this study, a novel piezoelectric energy harvester based on a perforated double-pillars metamaterial plate with a point defect, which offers the advantage of efficiently harvesting both ambient acoustic and flexural wave energy, is proposed. The proposed structure incorporates a locally resonant mechanism that enhances the concentration of vibration energy at the defect band frequency. Then, the amplified wave energy is efficiently converted into electrical energy by attaching a piezoelectric patch at the defect position. To initiate this investigation, the differential quadrature method is employed to theoretically estimate the boundary frequencies of the first band gap. Subsequently, this study investigates how holes size, electrical boundary conditions, and electrical circuit connections affect the energy harvesting of both acoustic and flexural waves. Correspondingly, the mechanisms behind their effects are thoroughly explained. Numerical results demonstrate that the wave energy localization performance can be remarkably amplified with an increasing holes radius, and the harvesters with the 1mm holes radius generate voltages that are approximately 2.12 and 1.44 times higher than those with the 0mm holes radius from acoustic and flexural waves, respectively. Furthermore, variations in the defect band frequency and corresponding wave localization behavior depend on the specific electrical boundary conditions and circuit connection approaches, ultimately leading to distinct results in the output electrical energy. These findings present valuable insights and guidelines for the development of high-performance electronic applications in the context of acoustic and elastic wave energy harvesting.

Analysis and simulation of X-band high-power microwave generation based on T-shaped four-period slow-wave structure

In this study, a T-shaped, four-period resonant slow-wave structure is optimally designed, and its high-frequency performance is comprehensively analyzed in theory. By using the image theory, the T-shaped waveguide unit is transformed into an equivalent ridge waveguide configuration. The high-frequency characteristics of the equivalent ridge waveguide, such as resonant frequency and structure of the T-shaped waveguide are analyzed by using equivalent circuit theory. The analysis has confirmed that in the ridge waveguide, starting from the second-highest order mode, the frequency points of the even-order modes are very consistent with those of the T-shaped waveguide; however, the odd-order modes have no such corresponding mode in the T-shaped waveguide, for they do not fulfill the electric boundary conditions required by the image method. On this basis, a T-shaped four-period resonant slow-wave structure is constructed, and its dispersion characteristics are analyzed to determine the resonant modes and frequencies, as well as the range of mode synchronization voltages. Simulations are subsequently performed to validate the effectiveness of the relativistic extended interaction radiation source, which includes the novel T-shaped periodic resonant slow-wave structure. Advanced three-dimensional particle simulations, in conjunction with optimization techniques show that a high-power microwave output at a frequency of 9.8 GHz, is achieved, which can delivers an average power of 71.4 MW. This output is attained under the conditions of a 448 kV beam voltage, 400 A beam current, and a 0.4 T uniform axial magnetic field, with an electron efficiency reaching 39.8%. This structure, characterized by the T-shaped waveguide, is demonstrated to be capable of producing high-efficiency, high-power microwaves with fewer periods, presenting a compact and efficient solution for generating high-power microwaves in advanced scientific applications.

Levy-type analytical series solution for the three-dimensional free vibrations of functionally graded material rectangular plates with piezoelectric layers

Analytical solutions founded on three-dimensional theories play a crucial role in evaluating the credibility and precision of different plate theories and numerical methodologies. While Levy-type analytical solutions are widely recognized, they have been primarily confined to purely elastic plates. This study introduces a Levy-type analytical series solution for three-dimensional vibrations in a sandwich rectangular plate featuring a functionally graded material (FGM) core, along with piezoelectric material (PM) layers on the top and bottom surfaces. The behaviors of the FGM and PM layers were described using three-dimensional elasticity and piezoelasticity theories, respectively. In this study, the displacement functions and electric potential of each layer were expanded by Fourier series and polynomial auxiliary functions. An analytical series solution was then established by satisfying the governing equations of each layer, the mechanical and electric boundary conditions on the six faces of the plate, and the continuity conditions on the interfaces between the PM and FGM layers. To validate the proposed solutions, in-depth convergence studies were conducted for the vibration frequencies of the first six modes of sandwich square plates with various boundary conditions on the other pair of side faces. The well-converged results were then compared with published data based on various plate theories to verify the accuracy of these published data. Finally, accurate nondimensional frequencies were tabulated for the first six modes of sandwich rectangular plates with various aspect ratios, thickness-to-width ratios, PM-to-FGM layer thickness ratios, power law indices for the FGM layer, and six combinations of boundary conditions. These new numerical results when piezoelectric coupling is considered should be very useful to future analytical and numerical studies.

Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals

AbstractThe present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.

Tensor-conductance model for reducing the computational artifact in target tissue for low-frequency dosimetry

Objective. In protecting human from low-frequency (<100 kHz) exposure, an induced electric field strength is used as a physical quantity for assessment. However, the computational assessment suffers from a staircasing error because of the approximation of curved boundary discretized with cubic voxels. The international guidelines consider an additional reduction factor of 3 when setting the limit of external field strength computed from the permissible induced electric field. Here, a new method was proposed to reduce the staircasing error considering the tensor conductance in human modeling for low-frequency dosimetry. Approach. We proposed a tensor-based conductance model, which was developed on the basis of the filling ratio and the direction of the tissue interface to satisfy the electric field boundary condition and reduce staircasing errors in the target tissue of a voxel human model. Main results. The proposed model was validated using two-layer nonconcentric cylindrical and spherical models with different conductivity contrasts. A comparison of induced electric field strengths with solutions obtained using an analytical formula and finite element method simulation indicated that for a wide range of conductivity ratios, staircasing errors were reduced compared with a conventional scalar-potential finite-difference method. The induced electric field in a simple anatomical head model using our approach was in good agreement with finite element method for exposure to uniform magnetic field exposure and that from coil, simulating transcranial magnetic stimulation. Significance. The proposed tensor-conductance model demonstrated that the staircasing error in an inner target tissue of a voxel human body can be reduced. This finding can be used for the electromagnetic compliance assessment and dose evaluation in electric or magnetic stimulation at low frequencies.

Finite element-based diffraction correction for piezoelectric transducers accounting for diffraction at transmission, propagation, and reception.

Existing diffraction correction models for ultrasonic transmit-receive measurement systems rely on simplifying assumptions with respect to the boundary conditions at the transmitter or receiver. Common simplifications include approximating the sound field radiated by a piezoelectric transducer using a baffled piston model and assuming that the receiver's electrical response is proportional to the spatially averaged free-field pressure over its front surface. In many applications, such simplifications may be adequate, but their validity and accuracy need to be evaluated and quantified. Here, a diffraction correction model utilizing the full set of electrical and mechanical boundary conditions at the transmitter and receiver is presented, avoiding these simplifications. The model is based on finite element modeling of coaxially aligned piezoelectric transducers in a fluid medium. Comparison is made with existing models for an example case of cylindrical piezoelectric ceramic disk transducers operating in air at 50-300 kHz and 0.03-2 m apart, relevant for, e.g., sound velocity and absorption measurements in fluids and ultrasonic gas flow metering. In the near-field, errors introduced by the simplifications are up to 3 dB and 47° for the first radial resonance. Generally, such errors are application-specific and depend on distance, frequency, transducer construction, vibration pattern, and medium properties.

Manipulation of acoustic wave scattering from cylindrical shells using a coating of FG magneto-electro-elastic composite materials: Active acoustic cloaking

Acoustically cloaking an object from view of a system that uses acoustic waves for detection is an attractive and practical capability. The aim of the current investigation is to hide a steel cylinder containing axial flow acoustically, which is achieved through the application of a coating of FG electro-magnetic material. This coating is employed to minimize the sound pressure that is scattered from the structure, and it comprises piezoelectric (BaTiO3) and magnetostrictive (CoFe2O4) make up the coating. Accordingly, the method presented is based on optimal control and incorporates an improved particle swarming optimization algorithm. The decision variables are the magnetic and electrical potentials on the inner and outer surfaces of the coating, whereas the cost function is the scattered acoustic pressure. In other words, what are the values of electrical and magnetic potentials on the inner and outer surfaces of the coating to minimize the scattered pressure? Subsequently, by defining the electrical and magnetic boundary conditions in a certain way, it is feasible to achieve the complete cancelation of scattered sound pressure. The governing equation of each layer is extracted using an orthotropic laminate composite model that is based on the 3-D theory of elasticity. A state-vector method is then applied to obtain the propagator matrix that links the state variables at each layer's surfaces. The results show that the proposed acoustic cloaking technique has an excellent capability for hiding the shell immersed in the fluid.

Reflection, transmission, and dissipation of plane waves in sandwiched functionally graded thermo- electro-elastic nanoplates via nonlocal integral elasticity theory

On account of the Lord-Shulman thermo-electric-elastic (TEE) theory and the nonlocal integral elasticity effect, the propagation of the plane wave in sandwiched functionally graded material (FGM) nanoplates, especially its energy dissipation, is investigated. A mathematical model is established by using the extended Legendre polynomial series approach. After imposing the mechanical, electrical and thermal boundary conditions by using the Legendre series, the reflection and transmission as well as the dissipation energy ratios are obtained. The influences of the nonlocal effect, relaxation time, gradient index, and electric filed are discussed. It is found that the nonlocal effect on the reflection of P waves is consistent with their transmission, but opposite to reflection of SV waves. Meanwhile, the nonlocal effect increases the dissipation. Besides, the dissipation variation in the normal incidence mainly comes from the transmission waves. The study is beneficial for the design of wave characteristics in TEE FGM nanoplates.

Electrokinetic ion rectification coupled with surface charge and thermal dependence in the conical nanochannel

With the further development of nanotechnology, electrokinetic ion rectification (ICR) is receiving increasing attention. Since the chemical equilibrium boundary is more suitable for expressing the wall charging characteristics and the coincidence of asymmetric temperature with ICR, we first propose an ICR ion transport model that couples the chemical equilibrium boundary with asymmetric temperature. In this work, ICR under different electrical boundary conditions is studied. The effects of membrane thermal conductivity, solution pH, and geometric conditions on the rectification performance are further explored in combination with surface charge and temperature dependence. The results show that the rectification ratio of the constant σ model and constant ζ model has a significant deviation compared to the multi-ion model, and the electrical boundary conditions can be simplified by changing the external conditions. By controlling the thermal conductivity of the membrane, the distribution of temperature difference within the reservoir or nanochannel can be determined, which affects the enrichment or depletion of ions in the nanochannel and ultimately achieves the goal of optimizing the rectification ratio. The optimal ICR ratio can be obtained by adjusting pH, and optimizing geometric conditions can significantly improve rectification performance. These studies provide helpful information for ion transport control and optimization of micro/nanofluid devices.