Electromechanical Phenomena Research Articles

On-Chip Microwave Frequency Combs in a Superconducting Nanoelectromechanical Device.

Nanomechanical resonances coupled to microwave cavities can be excited, measured, and controlled simultaneously using electromechanical back-action phenomena. Examples of these effects include sideband cooling and amplification, which are commonly described through linear equations of motion governed by an effective optomechanical Hamiltonian. However, this linear approximation is invalid when the pump-induced cavity microwave field is large enough to trigger optomechanical nonlinearities, resulting in phenomena like frequency combs. Here, we employ a niobium-based superconducting electromechanical device to explore the generation of microwave frequency combs. We observe the formation of combs around a microwave resonant frequency (3.78 GHz) with 8-MHz frequency spacing, equal to the mechanical resonant frequency. We investigate their dynamics for different optomechanical parameters, including detuning, pump powers, and cavity decay rates. Our experimental results show excellent agreement with numerical modeling. These electromechanical frequency combs can be beneficial in nanomechanical sensing applications that require precise electrical tracking of mechanical resonant frequencies.

Nonlinear features and energy transfer in an Acoustic Black Hole beam through intentional electromechanical coupling

Acoustic Black Hole (ABH) phenomenon features unique wave retarding and energy focusing of flexural waves inside thin-walled structures whose thickness follows a power-law variation. Existing studies, mostly focusing on linear aspects, show the deficiency of the linear ABH structures in coping with low-frequency problems, typically below the so-called cut-on frequency. In this paper, electrical nonlinearities are intentionally imposed via PZT patches over an ABH beam to tactically influence its dynamics through electromechanical coupling. Using a fully coupled electromechanical beam model, typical electromechanical coupling phenomena between the beam and the external nonlinear circuits, as well as the resultant salient nonlinear features of the system, are numerically investigated. Results show the beneficial effects arising from the intentional electrical nonlinearity in terms of generating energy transfer from low to high frequencies inside the beam, before being dissipated by the ABH covered by a small amount of damping materials. As such, the effective frequency range of the ABH is broadened, conducive to low-frequency vibration control problems. Meanwhile, different from existing mechanical means, the introduced intentional electrical nonlinearity allows for flexible tuning to accommodate specific frequency ranges arising from different applications.

Computation of flexoelectric coefficients of a MoS2 monolayer with a model of self-consistently distributed effective charges and dipoles.

Flexoelectricity is an electromechanical coupling phenomenon that can generate noticeable electric polarization in dielectric materials for nanoscale strain gradients. It is gaining increasing attention because of its potential applications and the fact that experimental results were initially an order of magnitude higher than initial theoretical predictions. This stimulated intense experimental and theoretical research to investigate flexoelectric coefficients in dielectric materials such as two-dimensional materials. In this study, we concentrate on the calculation of the flexoelectric coefficients of 2D-MoS2 due to a model using self-consistently determined charges and dipoles on the atoms. More specifically, we study the importance of two contributions that were neglected/omitted in previous papers using this model, namely, the charge term in the total polarization and the conservation of electric charge through a Lagrange multiplier. Our calculations demonstrate that the results for flexoelectric coefficients computed with this improved definition of polarization agree better with experimental measurements, provided that consistent definitions for signs are used. Additionally, we show how two physical contributions with opposite signs compete to give net values of flexoelectric coefficients that can be either positive or negative depending on their relative importance and give net values for the case of MoS2.

Investigation of a nonlinear piezoelectric energy harvester with advanced electric circuits with the finite element method

In this contribution, a system simulation method based on the finite element method (FEM) is applied to simulate a strongly coupled bimorph piezoelectric vibration-based energy harvester (PVEH) with various nonlinear, non-ideal and active circuits: The standard circuit, the synchronized switch harvesting on inductor circuit and the synchronized electric charge extraction circuit are considered. Furthermore, nonlinear elastic behavior of the piezoelectric material is taken into account and harmonic base excitations of different magnitudes at a fixed frequency are applied. The holistic FEM-based system simulation approach solves the complete set of piezoelectric equations together with the equation of the electric circuit such that all electromechanical coupling phenomena are taken into account. This fully coupled numerical analysis enables the detailed evaluation of the influences of the electric circuits on the vibrational behavior and the harvested energy of the PVEH with respect to the magnitude of base excitation. Results from literature on the efficiency of electric circuits are confirmed and interactions between mechanical and electrical nonlinearities of PVEHs are revealed.Article highlightsSystem simulations of a mechanically and electrically nonlinear piezoelectric energy harvester are performed using only one software tool.The infuence of electric circuits on the vibration behavior and the effciency of an energy harvester are investigated in detail.Interactions between mechanical and electrical nonlinearities of an energy harvester are revealed.

Parallel Simulation of The Electromechanical Transient Phenomena of Power System via Modern Software Development Technique

The simulation of power system electromechanical transient phenomena is highly dependent on the knowledge and model of special domain. For this reason, traditional parallelization of the simulation must be coupled with concrete algorithm and code. In this paper, a parallelized electromechanical transient simulation program is proposed based on the open-source simulation engine called InterPSS and general open object-oriented modelling framework. The correctness and effectiveness of this framework have been verified by a large-scale simulation case.

Influence of flexoelectricity on an interface crack between two dissimilar dielectric materials

In the present paper, the interface crack between two dissimilar dielectric materials under a mechanical load is investigated with including flexoelectricity effects. Flexoelectricity is a size dependent electro-mechanical coupling phenomenon, where the electric polarization is induced by a strain gradient in dielectrics. The strain gradients may potentially break the inversion symmetry in centrosymmetric crystals and polarization is observed even in all dielectric materials. The polarization is proportional to the strain gradients in the direct flexoelectricity. Layered composite structures are frequently utilized in microelectronics. Due to a poor adhesion of protection layer and basic material, the interface crack can be created there and for the prediction of failure of these structures it becomes essential to investigate distribution of the interfacial stress and strain fields.Governing equations in the gradient theory contain higher-order derivatives than in the standard continuum mechanics. Therefore, a reliable computational tool is required to solve these boundary-value problems. The mixed finite element method (FEM) is developed, where the standard C° continuous finite elements are utilized for independent approximations of displacements and strains. The constraints between the strain gradients and displacements are satisfied by collocation at Gaussian integration points inside elements. In numerical examples, a parametric study is performed with respect to flexoelectric and elastic coefficients for both material regions. The influence of these parameters on the crack opening displacement is discussed.

Control of cascading failures in dynamical models of power grids

In this paper, we introduce a distributed control strategy to prevent dynamically-induced cascading failures in power grids. We model power grids using complex networks and nonlinear dynamics to provide a coarse-grained description of the electro-mechanical phenomena taking place on them (in particular, we use coupled swing equations) and restrict our analysis to cascades of line failures, i.e., failures due to power flows exceeding the maximum capacity of a line. We formulate a distributed control protocol relying on the same topology of the physical layer and apply it to several power grid models, including a small-size illustrative example with five nodes, the Italian high-voltage (380kV) power grid, and the IEEE 118-bus system. Our results indicate that the approach is capable of preventing cascading failures, either controlling each node of the network or a suitable subset of them.

Reflection and transmission of waves at the common interface of piezoelectric half-spaces with microstructure

The present article deals with the reflection and transmission of waves at an interface of piezoelectric (ALN & PZT-5T) half-spaces with microstructures. Unlike the classical piezoelectric material, in the considered media, five coupled waves (2 bulk and 3 surface) [namely the Quasi-longitudinal wave (QP), Quasi-transverse wave (QSV), Electric-acoustic wave (EA), P-type surface wave (SP) and S-type surface wave (SS)] are generated in response to an oblique incident Quasi plane wave. The main objective of this study is to investigate the influence of the characteristic length of microstructure, the inertial characteristic length and flexoelectric coefficients on the reflection and transmission coefficients. For this purpose, the linear algebraic equation, continuity conditions at the common interface are contracted. The linear system of equations comprising the reflection and transmission coefficients is derived, which is solved by using the Cramer's rule. The consequence of this electromechanical phenomenon may be advantageous in certain engineering applications that involve smart nano-composites.

Multi-fidelity black-box optimization for time-optimal quadrotor maneuvers

We consider the problem of generating a time-optimal quadrotor trajectory for highly maneuverable vehicles, such as quadrotor aircraft. The problem is challenging because the optimal trajectory is located on the boundary of the set of dynamically feasible trajectories. This boundary is hard to model as it involves limitations of the entire system, including complex aerodynamic and electromechanical phenomena, in agile high-speed flight. In this work, we propose a multi-fidelity Bayesian optimization framework that models the feasibility constraints based on analytical approximation, numerical simulation, and real-world flight experiments. By combining evaluations at different fidelities, trajectory time is optimized while the number of costly flight experiments is kept to a minimum. The algorithm is thoroughly evaluated for the trajectory generation problem in two different scenarios: (1) connecting predetermined waypoints; (2) planning in obstacle-rich environments. For each scenario, we conduct both simulation and real-world flight experiments at speeds up to 11 m/s. Resulting trajectories were found to be significantly faster than those obtained through minimum-snap trajectory planning.

Compact explicit matrix representations of the flexoelectric tensor and a graphic method for identifying all of its rotation and reflection symmetries

Flexoelectricity is an electromechanical phenomenon produced in a dielectric material, with or without centrosymmetric microstructure, undergoing a non-uniform strain. It is characterized by the fourth-order flexoelectric tensor, which links the electric polarization vector with the gradient of the second-order strain tensor. Our previous work [H. Le Quang and Q.-C. He, Proc. R. Soc. A 467, 2369 (2011)] solved the fundamental theoretical problem of determining the number and types of all rotational symmetries that the flexoelectric tensor can exhibit. In the present study, compact explicit matrix representations of the flexoelectric tensor are provided so as to facilitate the use of it with any possible rotational symmetry. The number and types of all reflection symmetries that the flexoelectric tensor can have are also determined. To identify the rotational symmetry and reflection symmetry of a given flexoelectric tensor, a simple and efficient graphic method based on the concept of pole figures is presented and illustrated.

In situ and operando force‐based atomic force microscopy for probing local functionality in energy storage materials

AbstractElectrochemical energy storage is the key enabling component of electric vehicles and solar‐/wind‐based energy technologies. The enhancement of energy stored requires the detailed understanding of charge storage mechanisms and local electrochemical and electromechanical phenomena over a variety of length scales from atoms to full cells. Classical electrochemical techniques, such as voltammetry, represent the macroscopic electrochemical properties, and consequently do not allow to extract important information about local electrochemical reactions, ions adsorption, intercalations, and transport. Understanding, controlling, and tuning the local electrochemical functionalities in functional energy materials require in situ/operando techniques which limit the use of structural and functional characterization techniques that provide local information. Here, force‐based atomic force microscopies (AFMs) have provided novel insights into locally probing electrochemical mechanisms on tens of nanometer and even molecular length scales and provide a viable pathway to probe electrochemical processes in situ/operando. In this review, we highlight the contributions in the development and application of force‐based AFM methods to elucidate the local charge storage mechanism in a variety of energy‐related materials. We will focus in particular on methods or AFM modalities in a liquid electrolyte environment.

Flexoelectricity in metals

Flexoelectricity is an electromechanical phenomenon that, unlike piezoelectricity, is present in any material. While the largest flexoelectric response is observed in ferroelectrics and related materials, its manifestations in various other materials are of great interest for a broad scope of scientific and industrial tasks. Here, we provide a simple theoretical model for flexoelectricity in metals. This is done in terms of continuum mechanics. Estimates for aluminum are provided, and guidelines for an experimental detection of the phenomenon are formulated. The magnitude for the flexoelectric effect in metals is found to be comparable with that in high-k dielectrics, which makes metals just as good as other materials for applications in flexoelectric sensing and energy harvesting. Besides, in metals, flexoelectricity may be easier to interpret because it is predicted to be free of surface contributions.

Simulation of Low Inertia Power Systems Based on Shifted Frequency Analysis

New types of power system transients with lower time constants are emerging due to the replacement of synchronous generation with converter interfaced generation and are challenging the modeling approaches conventionally applied in power system simulation. Quasi-stationary simulations are based on classical phasor models, whereas EMT simulations calculate the instantaneous values of models in the time domain. In addition to these conventional modeling approaches, this paper investigates simulation based on dynamic phasor models, as has been proposed by the Shifted Frequency Analysis. The simulation accuracy of the three modeling approaches was analyzed for characteristic transients from the electromagnetic to the electromechanical phenomena range, including converter control as well as low inertia transients. The analysis was carried out for systems with converter interfaced and synchronous generation whilst considering the simulation step size as a crucial influence parameter. The results show that simulations based on dynamic phasors allow for larger step sizes than simulations that calculate the instantaneous values in the time domain. This can facilitate the simulation of more complex component models and larger grid sizes. In addition, with dynamic phasors, more accurate simulation results were obtained than with classical phasors, in particular—but not exclusively—in a low inertia case. Overall, the presented work demonstrates that dynamic phasors can enable fast and accurate simulations during the transition to low inertia power systems.

Multi-scale formulation of admittance-based modeling of cables

This paper proposes a novel multi-scale cable model in phase-coordinates exploiting the fully-coupled structure of the nodal admittance matrix instead of using the conventional approach based on the Method of Characteristics (MoC). The usage of the admittance modeling allows a straightforward representation of cables regardless of their lengths as it does not require a minimum time-step below the transient time associated with the fastest mode. In addition, some accuracy issues regarding the rational modeling of the nodal admittance matrix are overcome resorting to the Folded Line Equivalent (FLE) transformation.Following the so-called frequency-adaptive simulation of transients (FAST) concept, the trapezoidal rule and recursive convolution expressions are rewritten to perform computations using analytic signals or complex variables. This will allow the possibility to combine electromagnetic and electromechanical trasients phenomena in the same simulation environment with a unique mathematical model.A novel variable time-step algorithm is presented and its flexibility is so general that can be incorporated in Electromagnetic Transient (EMT) software such as EMTP-RV, PSCAD or Hypersim in straightforward way.Besides keeping the accuracy of the classic EMT-modeling, the proposed formulation provides a sensible gain in the overall computation time without significant loss of accuracy and also smooth transitions regardless of the time-step length.

Mechanical Manipulation of Silicon-based Schottky Diodes via Flexoelectricity

Silicon-based Schottky barrier diodes (SBDs), as a two-terminal circuit element, are widely used in modern industries due to its low cost and better compatibility with the complementary metal oxide semiconductor (CMOS) technology. Flexoelectricity resulting from strain gradient is a distinctive electromechanical coupling phenomenon compared to piezoelectricity resulting from strain. Flexoelectricity can exist in any dielectric due to the non-uniform strain breaking symmetry of materials. In this paper, we utilize the induced flexoelectric polarization to tune the behavior of a SBD made of metal and p-type Silicon. Making use of conductive atomic force microscopy (C-AFM), we measured current-voltage of the fabricated Si-based SBD under different tip forces. In order to conduct a quantitative study on the tuning effect of flexoelectricity on the performance of the fabricated Si-based SBD, we introduce an effective barrier height and provide a modified current equation according to the classical thermionic emission theory. The results show that flexoelectricity plays a significant role in dictating the Schottky barrier height, maximum rectified current (density), reverse saturation current (density), rectification ratio, and open voltage of the fabricated SBD. In addition, based on the Hertzian contact model and the measured data, the nonzero flexoelectric coefficients of the used p-type silicon are obtained.

Flexoelectric effects on the natural frequencies for free vibration of piezoelectric nanoplates

Flexoelectricity is an electromechanical coupling phenomenon between polarization and strain gradient. Based on the Kirchhoff thin plate theory, the electromechanical coupling responses of nanoplates with the piezoelectric and flexoelectric effects are studied in this paper. Free vibration of a piezoelectric nanoplate with consideration of flexoelectricity is analyzed with emphasis on the influence of the dynamic flexoelectric effect on the natural frequencies. By means of Hamilton’s variational principle, the governing equation of rectangular plates together with associated boundary conditions is derived. The natural frequencies are evaluated for a nanoplate simply supported at two opposite edges, and exact frequency equations are obtained for the other two opposite edges being simply supported, clamped–clamped, clamped–free, simply supported–free, or clamped–simply supported. The influence of dynamic flexoelectricity on the natural frequencies is elucidated. The results show that the dynamic flexoelectric effect is also size-dependent; the smaller the plate thickness is, the more obvious the dynamic flexoelectric effect is. The results also show that the dynamic flexoelectric effect is more pronounced when the order of vibration modes is higher and nanoplate’s side ratio is larger. The positive and negative choice of static and dynamic flexoelectric coefficients have completely different effects on the natural frequencies. The influence of the dynamic flexoelectric effect on the natural frequencies is closely related to the side constraint and geometry of the plate. The piezoelectric effect does not alter the natural frequencies for free vibration of a homogeneous nanoplate.

Conservation Integrals in Nonhomogeneous Materials with Flexoelectricity

The flexoelectricity, which is a new electromechanical coupling phenomenon between strain gradients and electric polarization, has a great influence on the fracture analysis of flexoelectric solids due to the large gradients near the cracks. On the other hand, although the flexoelectricity has been extensively investigated in recent decades, the study on flexoelectricity in nonhomogeneous materials is still rare, especially the fracture problems. Therefore, in this manuscript, the conservation integrals for nonhomogeneous flexoelectric materials are obtained to solve the fracture problem. Application of operators such as grad, div, and curl to electric Gibbs free energy and internal energy, the energy-momentum tensor, angular momentum tensor, and dilatation flux can also be derived. We examine the correctness of the conservation integrals by comparing with the previous work and discuss the operator method here and Noether theorem in the previous work. Finally, considering the flexoelectric effect, a nonhomogeneous beam problem with crack is solved to show the application of the conservation integrals.

Universal converse flexoelectricity in dielectric materials via varying electric field direction

ABSTRACT Flexoelectricity is a symmetry independent electromechanical coupling phenomenon that outperforms piezoelectricity at micro and nanoscales due to its size-dependent behavior arising from gradient terms in its constitutive relations. However, due to this gradient term flexoelectricity, to exhibit itself, requires specially designed geometry or material composition of the dielectric material. First of its kind, the present study put forward a novel strategy of achieving electric field gradient and thereby converse flexoelectricity, independent of geometry and material composition of the material. The spatial variation of the electric field is established inside the dielectric material, Ba0.67Sr0.33TiO3 (BST), by manipulating electrical boundary conditions. Three unique patterns of electrode placement are suggested to achieve this spatial variation. This varying direction of electric field gives rise to electric field gradient, the prerequisite of converse flexoelectricity. A multi-physics coupling based theoretical framework is established to solve the flexoelectric actuation by employing isogeometric analysis (IGA). Electromechanically coupled equations of flexoelectricity are solved to obtain the electric field distribution and the resulting displacements thereby. The maximum displacements of 0.2 nm and 2.36 nm are obtained with patterns I and II, respectively, while pattern III can yield up to 85 nm of maximum displacement.

Thickness-Dependent Piezoelectric Property from Quasi-Two-Dimensional Zinc Oxide Nanosheets with Unit Cell Resolution.

A quantitative understanding of the nanoscale piezoelectric property will unlock many application potentials of the electromechanical coupling phenomenon under quantum confinement. In this work, we present an atomic force microscopy- (AFM-) based approach to the quantification of the nanometer-scale piezoelectric property from single-crystalline zinc oxide nanosheets (NSs) with thicknesses ranging from 1 to 4 nm. By identifying the appropriate driving potential, we minimized the influences from electrostatic interactions and tip-sample coupling, and extrapolated the thickness-dependent piezoelectric coefficient (d33). By averaging the measured d33 from NSs with the same number of unit cells in thickness, an intriguing tri-unit-cell relationship was observed. From NSs with 3n unit cell thickness (n = 1, 2, 3), a bulk-like d33 at a value of ~9 pm/V was obtained, whereas NSs with other thickness showed a ~30% higher d33 of ~12 pm/V. Quantification of d33 as a function of ZnO unit cell numbers offers a new experimental discovery toward nanoscale piezoelectricity from nonlayered materials that are piezoelectric in bulk.

Numerical 3D Simulation of a Full System Air Core Compulsator-Electromagnetic Rail Launcher

Multiphysics problems represent an open issue in numerical modeling. Electromagnetic launchers represent typical examples that require a strongly coupled magnetoquasistatic and mechanical approach. This is mainly due to the high velocities which make comparable the electrical and the mechanical response times. The analysis of interacting devices (e.g., a rail launcher and its feeding generator) adds further complexity, since in this context the substitution of one device with an electric circuit does not guarantee the accuracy of the analysis. A simultaneous full 3D electromechanical analysis of the interacting devices is often required. In this paper a numerical 3D analysis of a full launch system, composed by an air-core compulsator which feeds an electromagnetic rail launcher, is presented. The analysis has been performed by using a dedicated, in-house developed research code, named “EN4EM” (Equivalent Network for Electromagnetic Modeling). This code is able to take into account all the relevant electromechanical quantities and phenomena (i.e., eddy currents, velocity skin effect, sliding contacts) in both the devices. A weakly coupled analysis, based on the use of a zero-dimensional model of the launcher (i.e., a single loop electrical equivalent circuit), has been also performed. Its results, compared with those by the simultaneous 3D analysis of interacting devices, show an over-estimate of about 10–15% of the muzzle speed of the armature.