Nonlinear Electromechanical Coupling Research Articles

Analysis of output characteristics of positive feedback piezoelectric energy harvester based on nonlinear magnetic coupling.

In light of the limitations of the current piezoelectric energy harvesters and the demand for self-power supply in wireless sensor nodes, a novel positive feedback piezoelectric energy harvester based on nonlinear magnetic coupling is proposed. The operational characteristics of this energy harvester are investigated from three perspectives: theory, simulation, and experiment. First, a nonlinear electromechanical coupling mathematical model that describes the dynamic response of the energy harvester system is established by combining the Hamilton variational principle with the piezoelectric theory. This provides a theoretical foundation for subsequent research. Second, finite element method simulations are employed to optimize the structural parameters of the energy harvester and study the impact of nonlinear magnetic force on its output performance. Finally, an experimental prototype is fabricated and an experimental test system is constructed to validate the designed positive feedback piezoelectric energy harvester. The results demonstrate that changes in the longitudinal beam angle have minimal effect on energy capture efficiency. By appropriately increasing the bending surface length, reducing initial magnetic moment, and augmenting mass block weight, wider working frequency bands and higher power generation capacity can be achieved when vibrating in low-energy orbits. The experimental findings align closely with theoretical design values and contribute to advancing broadband multi-directional piezoelectric energy harvesting technology in order to provide high-performance vibration-based power solutions for wireless applications.

Nonlinear analysis of unimorph piezoelectric nanobeam with a variable cross-section and flexoelectric effect

An analytical method is presented to investigate the nonlinear electromechanical coupling response of an unimorph piezoelectric nanobeam with a variable cross-section, taking into account the flexoelectric effect. Considering the geometric nonlinearity, strongly nonlinear governing equation with variable coefficients is derived using the energy variation method and solved by the differential quadrature method. The nonlinear effects of geometric nonlinearity, electromechanical loadings, flexoelectric effect and width ratio on the electromechanical coupling response are analyzed in detail. The results show that under different loadings, the flexoelectric parameter and width ratio have distinct effects on the electromechanical response of the piezoelectric variable cross-section nanobeam. When the mechanical loads are applied on the nanobeam, a larger flexoelelctric parameter results in a greater bending deflection and higher output of electric field and polarization. The width ratio of variable cross-section can also influence the bending deflection, but its impact on the output of electric field and polarization is limited. When the applied voltage loads are applied to the nanobeam, the bending direction can be controlled by the applied voltage, flexoelectric parameter or width ratio. Due to the strongly nonlinear governing equation, these results in this study differ significantly from those of piezoelectric nanobeam with uniform cross-section. This study can contribute to the understanding of electromechanical coupling response in piezoelectric variable cross-section nanobeam with flexoelectric effect. Additionally, it can be helpful in guiding the structure optimization of piezoelectric nanodevices.

Theoretical and experimental research on a Quasi-Zero-Stiffness-Enabled nonlinear piezoelectric energy harvester

Piezoelectric material provides a convenient and efficient avenue to convert ambient vibration energy into electrical energy to power wireless sensor network nodes of Internet of Things. However, the design of effective ultralow-frequency and low-amplitude harvesters using piezoelectric materials remains a challenge. To address this challenging problem, this paper devises a quasi-zero-stiffness-enabled (QZSE) piezoelectric energy harvester based on a geometrical nonlinear structure. The basic configuration and operation principles of the QZSE piezoelectric energy harvester ware elaborated firstly, then the nonlinear electromechanical coupling equation is derived, whose solution informs on both the dynamic and electrical responses of the harvester. The electromechanical-coupled equations are solved with the aid of the fourth-order Runge-Kutta algorithm. The energy harvesting performance is then investigated with respect to the parameter effects of excitation, damping and proof mass. For validating numerical results and demonstrating the advantages of the proposed design, a prototype is fabricated and experimentally tested. The results confirm the ability of the QZSE piezoelectric energy harvester in producing effective vibration-to-electricity energy conversion in ultralow frequency range. This study provides new impetus to energy harvesting from ultralow frequency ambient vibration using piezoelectric materials.

Performance analysis of nonlinear piezoelectric energy harvesting system under bidirectional excitations

In this paper, a cantilever beam piezoelectric energy harvester model of nonlinear partial differential equation based on Hamilton's Principle is established. A piezoelectric device using a bimorph cantilever beam with a fixed is subjected to horizontal and vertical excitation. Based on the Euler-Bernoulli thin beam model assumptions and inextensible deformation, the analysis further includes the effects of geometric nonlinearity and damping nonlinearity. The reduced-order nonlinear partial differential equations of motion with electro-mechanical coupling distributed parameter are derived by using Galerkin method. By using the method of multiple scales and solving the equations of motion, the energy harvester in its fundamental first-order resonance response is analyzed and the amplitudes of fundamental transverse deflection, output voltage and output power are determined. The major influence aspects of excitation amplitude, linear damping coefficient, nonlinear damping coefficient, impedance, nonlinear electro-mechanical coupling coefficient on transverse deflection, voltage and power are analyzed. The result shows that the linear damping coefficient and resistance affect the initial threshold of parametric excitation. The combination of parametric excitation and direct excitation gives full play to the advantages of parametric excitation and improve the energy conversion efficiency of the energy harvesting system.

Dynamic modeling with quantifying dissipated power density and experimental validation of dielectric elastomer actuators

This paper proposes a dynamic electromechanical model for dielectric elastomer actuators (DEAs) with dissipative processes. Dielectric loss of elastomers, resistance of electrodes, actuator geometry, elastomer viscoelasticity and nonlinear electromechanical coupling are considered, and a new visco-hyperelastic constitutive model with frequency-dependent parameters is developed for large-strain elastomers. The dynamic responses of DEAs at different driving frequencies are experimentally measured and comprehensively compared with those predicted results. The relative errors over the time period of 0–50 s at 5 and 7 Hz are respectively 3.6% and 3.4%, demonstrating the effectiveness of the model. The proposed dynamic model can not only predict the frequency response of DEAs but also characterize the creep and hysteresis behavior with reasonable accuracy. The power density dissipated during dielectric elastomer actuation is calculated and analyzed. The results suggest that selecting low-resistance electrodes and elastomers with short dielectric relaxation time and low viscous loss is a feasible way to achieve high energy conversion efficiency for DEAs. This work can be helpful for the design and control of DEAs, paving the way for their practical applications.

Mechanical Rectifier for Broadband Piezoelectric Vibration Energy Harvesting and Self-Adapting Synchronous Electric Charge Extraction

The synchronized switch interface circuit is believed to boost the piezoelectric power generation. The threshold voltage of electronic components causes rectification loss and delay of peak detection. This work reports a novel design of a mechanical rectification piezoelectric vibration energy harvester (MR-PVEH). Compact and low loss mechanical rectification is achieved by double switch with 5 electrodes contact at the cantilever tip. The switch as a mechanical stopper also contributes to broadband performance. The saturation voltage and response frequency range can be adjusted in modeling and simulation of nonlinear electromechanical coupling vibration. Self-adapting Mechanical rectification optimized synchronous electric charge extraction (M-OSECE) circuit is also proposed with less electronic components in this paper and shows an extra 60% increase in generated power than the traditional standard energy harvesting circuit (SEH) in test. This novel design gives a promising solution for self-adapting synchronous switching in broadband piezoelectric vibration energy harvesting.

Weight Shift Keying (WSK) With Practical Mechanical Receivers for Molecular Communications in Internet of Everything

Molecular communication (MC) is one of the emerging technologies enabling nanonetworks and the Internet of Everything (IoE). The practical implementation of the intra-body MC systems is crucial for realizing smart healthcare applications, i.e., drug delivery, early detection, and health monitoring, through communication between nanomachines. A Flexure field-effect transistor (FET) based MC receiver, providing high sensitivity by utilizing nonlinear electromechanical coupling, has recently been proposed. It can also identify neutral molecules, unlike bioFETs. Thus, virus or pathogen detection can be performed with onboard computing by these receivers placed in the Edge. To date, biosensor-based MC receivers have been analyzed only for concentration shift keying (CSK), although weight shift keying (WSK) is a very robust modulation technique. The Flexure-FET-based MC receiver is a great candidate for use in a WSK-based MC system since its transduction mechanism relies on the molecular weight. This work presents the first practical approach to a WSK-based MC system with an improved Flexure-FET-based MC receiver. Its key performance metrics are analyzed from a theoretical MC perspective, also considering biological interference to obtain a more realistic simulation.

Output characteristics analysis of pendulum type triboelectric nanogenerators considering nonlinear electromechanical coupling effects

In this study, output characteristics analysis of pendulum type triboelectric nanogenerators (P-TENG) considering nonlinear electromechanical coupling effects is conducted. Based on the analysis of power generation mechanism, an equivalent capacitance model is proposed. Combined with the energy principle and equivalent circuit method, an electromechanical coupling model considering the nonlinear variation of pendulum angle is established. Using the harmonic balance method (HBM) and alternated frequency/time domain technique, the steady-state output of the P-TENG is solved analytically, and the stability of the results is determined. Numerical integration and dynamic tests are used to verify the accuracy of HBM results. By comparing the changes in the P-TENG output performance with and without the nonlinear effect, it is shown that the model proposed in this study can effectively avoid the underestimation of the operation bandwidth (a relative increment of 83%) and significantly improve the accuracy of the P-TENG performance estimation. Based on these results, the influence of the design parameters (including excitation amplitude, damping ratio, gap length, and electrode angle) on the dynamic output characteristics of the system is discussed. The output performance of the P-TENG can be improved by increasing the excitation amplitude, reducing the damping ratio, and minimizing the electrode angle. In the actual design, the gap length and friction amplitude should be comprehensively considered to maintain the P-TENG output performance in a better state. Various fitting models have been proposed to model the relationship between the design parameters and output performance. The fitting coefficients obtained from the parameter influence discussion can be used as the basis for the P-TENG output performance design.

Enhanced DC power delivery from a rotational tristable energy harvester driven by colored noise under various constant speeds

This paper investigates the DC power delivery from a rotational tristable energy harvester (TEH) interfaced with a rectifier circuit driven by colored noise. The nonlinear electromechanical coupling equation of the rotational TEH under colored noise is derived, where the mutual coupling behavior caused by the rectifier circuit is also included. Then, the analytical expressions of the joint probability density function (JPDF) and mean DC power are derived under different constant speeds by using the stochastic averaging based on energy-dependent frequency. In order to enhance the DC power delivery, the effects of colored noise, rotational constant speed and structural parameters on dynamical behaviors and harvesting performance are analyzed. The obtained results suggest that by choosing an appropriate rotational speed or electromechanical coupling coefficient, the rectified voltage can reach the maximum while the JPDF has a symmetric tristable structure. The optimal nonlinear stiffness coefficients can be obtained by adjusting the position of the magnets to maximize the DC power. Unlike the monotonically decreasing rectification efficiency, the power conversion efficiency is approximately proportional to the time constant ratio. Therefore, a proper choice of time constant ratio is very important for the optimal design of the harvester. Finally, the numerical simulation and experimental results verify the effectiveness of the theoretical analysis.

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework, the Modal Electromechanical Coupling Factor (MEMCF) is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures. It is also an important tool to guide the piezoelectric damping design of linear structures. Advanced aircraft often fly in maneuvers, and the variable working conditions induce drastic changes in the load level on structures. Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated. To achieve a good vibration reduction effect covering all working conditions, one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures. Therefore, this paper defines the Nonlinear Modal Electromechanical Coupling Factor (NMEMCF) and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures. Three candidate definitions of the NMEMCF are given, including two frequency definitions and one energy definition. The energy definition is the most promising one. It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF. In addition, based on the energy formula, the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state. The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities. A strong correlation among the NMEMCF, geometric parameters, and energy dissipation is observed. The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping, especially for variable working conditions.

A fractional finite strain viscoelastic model of dielectric elastomer

Dielectric elastomer (DE) is an intelligent soft material and it is regarded as one significant artificial muscle. The nonlinear large deformation, electromechanical coupling and nonlinear viscoelasticity of DE material post great challenges for constitutive modeling and the associated dynamics. Fractional viscoelasticity has encountered some successes in the dynamics of complex materials. In the current study, a 3D constitutive relation of DE based on the fractional Kelvin-Voigt viscoelastic model by considering finite strain is established. The Cauchy stress under the condition of uniaxial and biaxial stretches is derived. The fractional dynamics equations of DE membrane are also formulated based on the virtual work principle. The composite integral rule for fractional derivative and the Runge-Kutta method are combined to numerically solve the dynamics system. The constitutive model is fitted to the uniaxial and biaxial stretch experimental data, and the material parameters are obtained. Subject to a cyclic deformation, the stress-softening effect of the DE membrane is simulated. Furthermore, the dynamics responses of DE membrane are also calculated. A convenient approach is given to evaluate the equilibrium point of the system. It reveals that the model could be used to predict the creep behaviors for both free vibration and parametric excitation vibration.

Nonlinear Dynamics of an Unsymmetric Cross-Ply Square Composite Laminated Plate for Vibration Energy Harvesting

The nonlinear behaviors and energy harvesting of an unsymmetric cross-ply square composite laminated plate with a piezoelectric patch is presented. The unsymmetric cross-ply square composite laminated plate has two stable equilibrium positions by applying thermal stress, thus having snap-through with larger amplitude between the two stable equilibrium positions relative to the general laminated plate. Based on the von-Karman large deformation theory, the nonlinear electromechanical coupling equations of motion of the unsymmetric composite laminated plate with a piezoelectric patch are derived by using Hamilton’s principle. The influence of the base excitation amplitude on nonlinear behaviors and energy harvesting are investigated. For different base excitation amplitudes, the motions of the system demonstrate periodic motion, quasi-periodic motion, chaotic motion and snap-through, and two single-well chaotic attractors and a two-well chaos attractor coexist. Moreover, the power generation efficiency is optimal when the excitation amplitude is in a certain range due to its own unique nonlinear characteristics. The unsymmetric cross-ply square composite laminated plate subjected to thermal stress can actually be called a kind of bistable composite shell structure that has a broad application prospect in combination with morphing aircraft, large deployable antenna and solar panel, which are very likely to have nonlinear vibration.

Viscoelasticity Modeling of Dielectric Elastomers by Kelvin Voigt-Generalized Maxwell Model.

Dielectric elastomers (DEs) are polymer materials consisting of a network of polymer chains connected by covalent cross-links. This type of structural feature allows DEs to generate large displacement outputs owing to the nonlinear electromechanical coupling and time-dependent viscoelastic behavior. The major challenge is to properly actuate the nonlinear soft materials in applications of robotic manipulations. To characterize the complex time-dependent viscoelasticity of the DEs, a nonlinear rheological model is proposed to describe the time-dependent viscoelastic behaviors of DEs by combining the advantages of the Kelvin–Voigt model and the generalized Maxwell model. We adopt a Monte Carlo statistical simulation method as an auxiliary method, to the best knowledge of the author which has never reportedly been used in this field, to improve the quantitative prediction ability of the generalized model. The proposed model can simultaneously describe the DE deformation processes under step voltage and alternating voltage excitation. Comparisons between the numerical simulation results and experimental data demonstrate the effectiveness of the proposed generalized rheological model with a maximum prediction error of 3.762% and root-mean-square prediction error of 9.03%. The results presented herein can provide theoretical guidance for the design of viscoelastic DE actuators and serve as a basis for manipulation control to suppress the viscoelastic creep and increase the speed response of the dielectric elastomer actuators (DEA).

Effect of Nonlinear Electromechanical Coupling in Magnetic Levitation Energy Harvester

This paper investigates the possibility of converting vibrations to electricity. A numerical and an experimental study of a magnetic levitation harvester are proposed. The system can be highly efficient when the electrical parameters are correctly tuned. Mechanical and electrical interaction of the harvester is described by an electromechanical coupling. Fixed value, linear and nonlinear electromechanical coupling models are presented and compared. It has been shown that the nonlinear electromechanical coupling model is more suitable for higher oscillations of the magnet. The obtained results show that nonlinear resonance and recovered energy can be controlled by the simple configuration of the magnet coil position. The recovered energy from the top branch is significantly higher, but this solution is much harder to obtain.

Nonlinear modeling of [formula omitted]-mode piezoelectric actuators using experimental vibration analysis

This article focuses on characterizing the nonlinear nature of the piezoelectric actuators’ ‘33’-electromechanical coupling and ‘3’-directional elasticity. Vibrations of a cantilever aluminum beam, attached with a pair of d33-mode surface bondable multilayer actuators, were studied to construct the required nonlinear constitutive equation. As both elasticity and electromechanical coupling were of equal interest, a sequential experimental procedure was followed to conduct an exclusive analysis of each of them. Accordingly, first, the actuators were short-circuited, and a set of displacement-frequency-response plots were obtained for the first and second bending modes. The profile of the backbone curve of the response plots revealed the presence and the nature of the nonlinearity in the elastic domain. Equipped with the knowledge of the nonlinear elastic behavior, nonlinearity in electromechanical coupling was then investigated from a set of response plots obtained through the piezoelectric actuation of beam. Here too, the profile of the backbone curves revealed the type of nonlinearity present in the electromechanical behavior. With the information obtained from these two steps, a final nonlinear constitutive equation was constructed to represent both the nonlinear elasticity and the nonlinear electromechanical coupling in the actuator.

Nonlinear modeling and study of rigid-flexible piezoelectric energy harvester with additional frame

Based on a rigid-flexible piezoelectric energy harvester (PEH) composed of antisymmetric double plates with a rigid frame, which has three operating bandwidths in a low-frequency range, nonlinearity is used to further broaden the operating bandwidth. Firstly, finite-element simulation is used to study the influence of structural parameters, such as the width of the frame and the distance between two plates, on the natural frequencies. Bending deformation of cantilever plates and rigid motion of frame are considered comprehensively to obtain the theoretical mode functions of the structure. The nonlinear electromechanical coupling model is established via von Karman nonlinear geometric assumptions and the Hamilton principle. In order to study the broadening of output bandwidth caused by nonlinearity, the average equations with 1:1.5:2 internal resonance ratio are derived by the multi-scale method. On the basis of the calculated optimal resistance, the voltage response and dimensionless amplitude response curves induced by the first three order modes are numerically calculated. Theoretical analysis shows that the proposed PEH not only obtains three peaks of voltage output in a low-frequency range, but also utilizes hard spring effect and internal resonance to widen the output bandwidth of each resonance interval.

Piezoelectric energy harvesting from nonlinear dynamics of functionally graded plate under multi-moving loads and masses

In this study, energy harvesting from nonlinear vibrations of a functionally graded plate with bonded piezoelectric patch under moving loads and moving masses is investigated. The coupled nonlinear system of equations are derived using the generalized Hamilton’s principle considering both the geometrical nonlinearity and the nonlinear electromechanical coupling. Then, the equations are solved using finite element method and Newmark time integration scheme. For a case study, the effects of different parameters such as piezoelectric patch thickness, location of piezoelectric patch, different boundary conditions, and different width of plate on harvested power and the plate’s nonlinear vibration are investigated. This article is motivated by the lack of published studies on nonlinear distributed piezoelectric energy harvesters under moving loads (masses).

Predicting energy harvesting performance of a random nonlinear dielectric elastomer pendulum

This paper investigates the energy harvesting (EH) performance of a nonlinear dielectric elastomer pendulum (DEP) under the random narrowband excitation. The DEP that can convert the vibration energy into electrical energy consists of a dielectric elastomer membrane with a mass, which is similar to a spring pendulum. A dynamic analysis model of the nonlinear electromechanical coupling behavior of the DEP under the random narrowband excitation is developed. A prototype of the DEP is designed to evaluate the developed dynamic model, which shows the good agreement. On this basis, the stochastic dynamic behavior of the DEP is analyzed by changing the intensity, the power spectrum density, and the upper limiting frequency of the random narrowband excitation. The EH performance of the DEP under the random narrowband excitation is also studied for diverse system parameters, including the length of the dielectric elastomer membrane, the mass of the DEP, and the load resistance. The conclusions can help guide the design of the DEP in the random vibration environment to improve the EH performance.

Disturbance rejection control for PMSM using integral sliding mode based composite nonlinear feedback control with load observer

The low-speed high-torque permanent magnet synchronous motor (PMSM) drive system is a kind of typical nonlinear, strong-coupling and easy-parameter perturbation electromechanical coupling system. The control system is uncertainties and subject to unknown external interferences as well. In this paper, a disturbance rejection control method combining robust speed controller and load observer is proposed for low-speed high-torque PMSM. The robust speed controller combines the composite nonlinear feedback (CNF) which has advantage in improving the transient responsive performance and the integral sliding mode (ISM) advancing in improving system robustness. Subsequently, the effects of unknown external interferences are avoided by using a sliding mode observer (SMO), in which the chattering is reduced by introducing fuzzy control, and the observation is used for feed-forward compensation. The proposed robust speed controller solves the contradiction between the rapidity and overshoot of the traditional control method, and combines the load observer to compensate the influence of the load mutations and wide range of the load changes on the control system. Finally, the numerical simulation and experiments demonstrate that the proposed speed control method is able to achieve good transient performance in inhibiting system overshoot and reducing stable state error. Additionally, it successfully suppresses the influence of load disturbances and mutations, and shows the proposed method has better robustness.

Frequency-dependent nonlinear electromechanical coupling behaviors of ferroelectric composites

In this paper, a frequency-dependent micromechanics-based model is developed to study the nonlinear electromechanical coupling behaviors of ferroelectric composites which in general consist of ferroelectric inclusions and a polymer matrix. The coupling behavior not only depends on the volume concentration and the shape of the inclusions, but also on the frequency of external applied field. For the frequency-dependent properties, an exponential function is introduced to evaluate the remanent polarization and coercive field of the ferroelectric phase. Then a two-level micromechanics-based model is applied to obtain the hysteresis loops and butterfly-shaped responses of the ferroelectric composites at various frequencies. The first level model deals with the single ferroelectric phase by considering the evolution of domain switches while the second level is regarding to the two-phase ferroelectric composites. To verify the developed theory, we compared the calculated results with the existing experimental data for the hysteresis of electric displacement versus electric field and the butterfly-shaped strain versus electric field of the 1–3 type of composites with PZT fibers embedded in an epoxy matrix. The comparisons between theoretical calculations and experimental data show reasonable agreement. In the meantime, the influences of the shape and the volume concentration of the inclusions to the overall effective properties of the composites have been investigated and will shed the light for the design and structure architecture of the ferroelectric composites.