Electromechanical Analogy Research Articles

A Frequency Up-Conversion Piezoelectric Energy Harvester Shunted to a Synchronous Electric Charge Extraction Circuit.

A frequency up-conversion piezoelectric energy harvester (FUC-PEH) consists of a force amplifier, a piezoelectric stack, a low-frequency oscillator (LFO), and a stop limiter. The force amplifier generates the amplification of stress on the piezoelectric stack. The LFO, comprising a spring and a mass block, impacts the stop limiter during vibration to induce high-frequency oscillations within the piezoelectric stack. In this paper, we represent and simplify the FUC-PEH as a lumped-parameter model based on piezoelectric material constitutive equations and structural dynamic theories. Using the electromechanical analogy, we developed an equivalent circuit model (ECM) of the FUC-PEH. A parametric study was performed to investigate the impact of system parameters, such as spring stiffness and concentrated mass, on the FUC-PEH performance. The collision-induced amplitude truncation (AT) effect enlarges the operation bandwidth. ECM simulations show that low-frequency input excitation is converted into a high-frequency output response, enhancing the energy conversion efficiency. Furthermore, we aimed to improve the FUC-PEH's performance using a synchronous electric charge extraction (SECE) circuit. Using the ECM approach, we established a system-level model that considers the electromechanical coupling behavior. The simulation results provide insights into the performance of FUC harvesters with SECE circuits and offer valuable design guidance.

A locally resonant metamaterial beam with tunable electromagnetic stiffness based on the electromechanical analogy network

Locally resonant acoustic metamaterials offer distinctive advantages in controlling low-frequency elastic waves. However, passive structures often face limitations due to narrow bandgaps and fixed working band once they are fabricated. This paper introduces a novel metamaterial beam with tunable bandgaps. This achievement is made possible by employing one electromagnet and three permanent magnets to create an electromagnetic spring. The initial stiffness, provided by the spiral beam, collaborates with the electromagnetic components to establish a local resonant unite cell featuring tunable composite stiffness. Subsequently, an analogy network is formulated for the metamaterial beam based on electromechanical analogy theory. This network not only elucidates the generation mechanism and regulatory principles of bandgaps but also serves as a paradigm for the proactive design of the metamaterial beam with external control sources, particularly under finite period conditions. Finally, theoretical analysis and experimental results collectively demonstrate the flexibility of the proposed metamaterial beam in effectively suppressing low-frequency elastic waves across a wide frequency range.

Analysis of Coupled Vibration Characteristics of Linear-Angular and Parameter Identification

Abstract A steady-state sinusoidal and distortion-free excitation source is very important for the accuracy and consistency of the calibration parameters of micro-electro-mechanical systems (MEMS) inertial sensors. To solve the problem that the current MEMS inertial measurement unit (IMU) calibration device is unable to reproduce the spatial motion of linear and angular vibration coupling, research topics on the coupling vibration characteristics and parameter identification for an electromagnetic linear-angular vibration exciter are proposed. This research paper used Ampere’s law and Lorentz force to establish the analytical expressions for the electromagnetic force and electromagnetic torque of the electromagnetic linear-angular vibration exciter. Then, the main purpose of this paper is to establish uniaxial and coupled vibration electromechanical analogy models containing mechanical parameters based on the admittance-type electromechanical analogy principle, and the parameter identification model is also obtained by combining the impedance formula with the additional mass method. Finally, the validity of the coupling vibration characteristics and the parameter identification model are verified by the frequency response simulation and the additional mass method, and the relative error of each parameter identification is within 5% in this paper.

Electro-mechanical analogy for Prabhakar-like fractional viscoelasticity

The aim of this paper is to set up a formal equivalence between a mechanical system and an electrical one. Specifically, we consider the Maxwell-Prabhakar linear viscoelastic model, based on Prabhakar fractional operators. Therefore, we find the analogous expression for the electric current due to a step potential. The expression for the resulting electric current depends on the variable characterizing the viscoelastic model and its behaviour is then discussed with the support of some interesting plots.

Influence of Active-to-Passive Ratio on the Deformation in Circular Dielectric Elastomer Actuators.

To further improve the performance of dielectric elastomer actuaotrs (DEAs), the development of novel elastomers with enhanced electro-mechanical properties is focal for the advancement of the technology. Hence, reliable techniques to assess their electro-mechanical performance are necessary. Characterization of the actuator materials is often achieved by fabricating circular DEAs with the pre-stretch of the membrane fixed by a stiff frame. Because of this set-up, the electrode size relative to the carrier frame's dimension has an impact on actuator strain and displacement. To allow for comparable results across different studies, the influence of this effect needs to be quantified and taken into account. This paper presents an in-depth study of the active-to-passive ratio by proposing two simplified analytical models for circular DEA and comparing them. The first model is taking the hyperelastic material properties of the dielectric film into account while the second model is a linear elastic lumped parameter model based on the electro-mechanical analogy. Both models lie in good agreement and show a significant linear impact of the radial active-to-passive ratio on the electro-active strain and a resulting maximum of displacement around 50% radial coverage ratio. These findings are validated by experiments with actuators fabricated using silicone membranes. It is shown that the electrode size is not only an important parameter in the experimental design, but in some cases of higher significance for the accuracy of analytical models than the hyperelastic properties of the material. Furthermore, it could be shown that a radial coverage ratio of around 50% is desirable when measuring displacement as it maximizes the displacement and lowers the impact of deviations in electrode sizes due to fabrication errors.

Analogous piezoelectric network for multimodal vibration attenuation of a thin circular ring

Structural vibrations can be reduced by coupling to a piezoelectric electrical network that exhibits analogous modal properties of the structure. This paper considers the multimodal vibration damping of a thin circular ring using this method. The electrical network is derived by applying a finite difference model to the governing equations of motion for a segment of a thin curved beam. An electromechanical analogy is then applied to the physical constants. The resulting passive electrical network unit cell is a topology of capacitors, inductors, and transformers analogous to the dynamics of a segment of curved beam. The electrical network for a curved beam is simplified by considering an inextensional assumption and combining edge components in adjacent unit cells. The resulting simplified discrete network for a curved beam segment is assembled into a complete network for a circular ring. The electrical network for a circular ring displays modal properties similar to its mechanical analogue in both the spatial and frequency domains. As a result of the analogous modal properties across the frequency spectrum, it is shown that the network can be used to achieve multimodal vibration attenuation across a large frequency spectrum. Piezoelectric patches are used to couple the two domains. Numerical simulation of the coupled system demonstrates the effectiveness of the broadband damping effects from the analogous network. Notably, this research establishes a novelty in the field, as it not only introduces experimental validation of curved beam analogues, but also extends the investigation to encompass the coupling between a circular ring and its piezoelectric electrical network counterpart. Further experimental network optimization demonstrate the possibility of tuning the network to adapt to an imperfect mechanical ring.

Heterogeneous numerical modeling of fatigue damage for asphalt mixtures through complex mechanical impedances

Asphalt mixes, also known as bituminous concrete and asphalt concrete (AC), which are one of the most widely used materials in pavement engineering, are complex, multi-scale composite materials. AC is a heterogeneous material composed of a bituminous matrix and aggregates featuring viscoelastic and elastic behavior, respectively. Fatigue under cyclic loading of this material is one of the main pavement degradation phenomena. Under cyclic loading, the viscoelastic behavior of this material converts part of the energy brought by the loading into dissipated energy due to the viscous effects of the bituminous matrix. It is a heat source that leads to the increase of temperature during phase I of fatigue (self-heating). The second part of the energy is restituted and is the growth driving force of the damage. This work deals with a new thermodynamic approach to describe rheological models applied to viscoelastic materials under mechanical cyclic loading. The dissipation and the energy-released rate are determined based on an electromechanical analogy to simulate damage growth and the temperature increase. Both thermal and mechanical aspects and their coupling are taken into account leading to complete constitutive modeling to simulate the decrease of the AC complex modulus. Using the image processing technique, a heterogeneous microstructure is used to model the AC.

A comprehensive methodology to obtain electrical analogues of linear mechanical systems

Electrical analogues of linear mechanical systems have traditionally been obtained using a set of rules that can potentially be tedious when applied to complex systems. In addition, such rules do not cover all the possibilities of mechanical systems including rotational and translational generalized coordinates. The present work establishes a comprehensive and systematic methodology for obtaining the electrical analogue of any mechanical system modelled by rigid bodies, springs, and dampers. The method is simple and straightforward. First, the dynamic equations of the mechanical system are derived into matrix form. These equations are then translated to the electrical domain by means of the electromechanical analogy and, finally, the electrical circuit is obtained by direct inspection of the matrices. In addition, the method can deal with a combination of translational and rotational coordinates in the definition of the mechanical model. To support the proposed method, and beyond the planar vehicle models found in the literature, the electrical analogue of a linear 3D 7-DOF full car model is presented in this work.

Development and analysis of coatings cavitation erosion model by controlling changes in the acoustic properties of liquid media in limited volumes with resonant dimensions

The article considers the influence of the extent of cavitation wear of materials and their coatings on the acoustic properties of the sounded liquid media in a limited volume. The model of an liquid media bounded by a volume with resonant dimensions is considered based on an electromechanical analogy system. The parameters and characteristics of the sounded liquid media most sensitive to changes in the dimensions of the volumes confining them as a result of their cavitation erosion are determined.

A generalized electromechanical coupled model of standing-wave linear ultrasonic motors and its nonlinear version

For the systematization of research on standing-wave linear ultrasonic motors (SWLUMs), this work develops a generalized electromechanical coupled model for characterizing SWLUMs. The proposed model focuses on dealing with modeling the generalized two-stage energy conversion in SWLUMs. The first-stage energy conversion is modeled by a four-terminal equivalent circuit model, which with a phase shifter and a couple of electromechanical transformers based on the electromechanical analogy method. The second-stage energy conversion is modeled by a physics-based, friction-driven system, involving contact nonlinearities between the stator and the mover. Furthermore, the effectiveness of this model and its further extension considering nonlinear vibrations of piezoelectric transducer (stator) are exemplified and discussed by a classical SWLUM with V-configuration stator, thereby indicating that the presented generalized model is valuable and pragmatic in simulating and characterizing SWLUMs both in electrical and mechanical domains.

Modeling and Analysis of the Torque-Frequency Dynamics for Multi-VSC Parallel System Based on the Equivalent Admittance

The increasing use of voltage-source converters (VSCs) in modern power systems has led to extensive studies on their frequency response and stability, which are characterized by power-frequency oscillations and overshoots following a disturbance. However, the existing small-signal analysis models do not adequately describe the impact of the types of disturbance on the torque-frequency dynamics of the multi-VSC parallel system. In this paper, based on the principle of electromechanical analogy, a unified equivalent admittance modeling method is proposed by analogizing the rotor dynamic model of a synchronous generator (SG) to the circuit network, which has the advantages of simple modeling, clear physical meaning and easy expansion. Firstly, the equivalent admittance model of a single SG/VSC is established, and then easily extended to the multi-VSC system. The proposed modelling method not only applicable to a variety of VSCs, but also can handle different types of disturbance. More importantly, the circuit theory can be applied to analyze the torque-frequency dynamic characteristics. Subsequently, the equivalence between the proposed model and the state-space model under different damping terms is compared. In addition, the response characteristics of two different damping terms are compared. Next, the dynamic response characteristics of single VSC and multi-VSC parallel systems under different disturbances are analyzed. Finally, related simulations and experiments are executed to verify the accuracy and effectiveness of the proposed method.

RESONANT MODES OF A LINEAR PERMANENT MAGNET VIBRATORY MOTOR

The work considers the resonant operation modes of the linear permanent magnet vibratory motor. On the basis of electrical and mechanical equivalent circuits with lumped parameters, expressions for determining the frequencies of mechanical, electrical, energy and power resonances are obtained. The presence of two frequencies of electrical resonance (when the phases of supply voltage and motor current coincide) in a single-mass electromechanical system and four in a two-mass one is substantiated. Representing, according to the electromechanical analogy approach, the back EMF induced due to the movement of the mover by the corresponding voltage drop, expressions for equivalent mechanical impedances are obtained. The dependences of the energy characteristics of the motor (mechanical work and efficiency) on the equivalent circuit parameters are obtained. Based on the expression for the reluctance electromagnetic force, mechanical work is found and its dependence on the phase difference between displacement and current is shown. The phase difference at which the total mechanical work of the motor is maximal is determined. It is shown that the results of the analysis of resonant modes well agree with results of a numerical field study carried out on the basis of the equations of the quasi-stationary magnetic field in the time domain using the finite element method and the moving type of calculation mesh in the mover region. References 12, figures 6, tables 1.

Study of nonlinear vibration of resonant gyroscope based on uncertainty analysis method

To study the nonlinear vibration characteristics of resonant gyroscope, the vibration model of the resonant beam is established primarily, aiming for the analytical formulas of the nonlinear stiffness coefficients and linear intrinsic frequencies of the gyroscope. With that foundation, the influence of the structural parameters of the resonant beam on the frequency tracking error caused by nonlinear vibration is analyzed thoroughly at first. Secondly, by random sampling, an uncertainty analysis model is established to evaluate the impact of each structural parameter of the resonant beam on the critical performance indexes of the gyroscope such as linear intrinsic frequency, nonlinear frequency offset and scale factor of the resonant beam. Finally, an equivalent circuit is constructed corresponding to the nonlinear vibration equations of the resonant gyroscope based on the electromechanical analogy method. By studying the nonlinearity of the circuit for equivalence, it turns out that the vibration characteristics of the equivalent circuit are consistent with that of the resonant gyroscope obtained by using the uncertainty analysis method. It effectively verifies the feasibility of the nonlinear vibration research method for the resonant gyroscope based on uncertainty analysis method.

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To study the nonlinear vibration characteristics of resonant gyroscope, the vibration model of the resonant beam is established primarily, aiming for the analytical formulas of the nonlinear stiffness coefficients and linear intrinsic frequencies of the gyroscope. With that foundation, the influence of the structural parameters of the resonant beam on the frequency tracking error caused by nonlinear vibration is analyzed thoroughly at first. Secondly, by random sampling, an uncertainty analysis model is established to evaluate the impact of each structural parameter of the resonant beam on the critical performance indexes of the gyroscope such as linear intrinsic frequency, nonlinear frequency offset and scale factor of the resonant beam. Finally, an equivalent circuit is constructed corresponding to the nonlinear vibration equations of the resonant gyroscope based on the electromechanical analogy method. By studying the nonlinearity of the circuit for equivalence, it turns out that the vibration characteristics of the equivalent circuit are consistent with that of the resonant gyroscope obtained by using the uncertainty analysis method. It effectively verifies the feasibility of the nonlinear vibration research method for the resonant gyroscope based on uncertainty analysis method.

ОПТИМІЗАЦІЙНИЙ ПІДХІД ДО ВИЗНАЧЕННЯ КОНСТРУКТИВНИХ ПАРАМЕТРІВ ЛІНІЙНОГО МАГНІТОЕЛЕКТРИЧНОГО ДВИГУНА ВІБРАЦІЙНОЇ ДІЇ

The constructional parameters of the linear permanent magnet vibratory motor in accordance with the set optimization criteria (minimum cost, force to volume ratio and efficiency) and mechanical load parameters are substantiated in the work. To do this, a computer model was developed, which is based on magnetic and electrical equivalent circuits with lumped parameters. The magnetic circuit of the model is built taking into account the saturation of the magnetic material, magnetic losses and leakage fluxes. The electromagnetic force amplitude of the motor is determined on the basis of the fundamental component of the Fourier series expansion of the air-gap flux density. The mechanical part of the model is constructed using the electromechanical analogy method, according to which, induced armature EMF is represented by a voltage drop on the equivalent mechanical resistance. The problem of choosing the constructional parameters for the given mechanical load characteristics is considered in conjunction with the nonlinear connections of the system and subject to thermal, magnetic and electrical constraints. Using the gradient descent method, the motor parameters were optimized and the most effective designs that meet the selected criteria were determined. References 8, figures 5, tables 2.

MODELING OF DYNAMICS OF ELECTRODYNAMIC SPEAKER

This article discusses an electromechanical system in the form of an electrodynamic loudspeaker. To describe the dynamics of a loudspeaker, a finite-dimensional model with a given number of a finite number of independent mechanical and electrical parameters is used. Using the electromechanical analogy force - voltage and using the Lagrange-Maxwell equations, a closed system of two nonlinear differential equations of the second order of motion of the system is compiled. Using modern advances in computer technology, a number of numerical experiments were performed in the Mathcad system with varying values of the input parameters of the system, such as the mass of the moving coil, inductance, ohmic resistance, and graphs of the time variation of the coil movement and current strength were plotted. Phase portraits were also built. The movement of the system has the character of damped oscillations, and the phase portraits have a stable focus. The influence of the varied parameters on the period of damped oscillations and the transition of the system to the state of equilibrium is shown. The study was carried out for a nonlinear model without the use of asymptotic methods, which made it possible to exclude the methodological error of the solution. The model can exhibit complex dynamics. Having a mathematical model and a calculation program, it is possible to carry out further studies of the system under consideration, identifying the positions of stable and unstable equilibrium, modes of self-oscillations, defining areas of periodic and chaotic modes of different nature. The results obtained can be used in the development of technical devices capable of demonstrating complex behavior. Methodologically, the proposed material is interesting for undergraduate and graduate students specializing in electromechanics, in terms of teaching the principles of constructing and analyzing electromechanical systems.

Using an Electromechanical Analogy to Describe the Damping Characteristics of an MFC Actuator

In this article, a mathematical model was formulated that describes the dynamic behavior of MFC actuators. The model was developed on the basis of numerical-analytical methods for solving coupled boundary value problems of electromagnetoelasticity for inhomogeneous media equipped with piezoactive structural elements and loaded with coherent electromechanical disturbances. Within the framework of the performed numerical experiments, stationary harmonic axisymmetric oscillations of an elementary composite two-phase MFC actuator cell loaded with coherent electromechanical disturbances were considered. The calculation of the MFC actuators complex impedance and conductivity values, taking into account the energy losses and phase shift at different levels of the control electric voltage, was carried out.

Design and test study of a new mixed control method for magnetorheological semi-active suspension based on electromechanical analogy theory

Design and test study of a new mixed control method for magnetorheological semi-active suspension based on electromechanical analogy theory

A New Electromechanical Analogy Approach Based on Electrostatic Coupling for Vertical Dynamic Analysis of Planar Vehicle Models

Analogies between mechanical and electrical systems have been developed and applied for almost a century, and they have proved their usefulness in the study of mechanical and electrical systems. The development of new elements such as the inerter or the memristor is a clear example. However, new applications and possibilities of using these analogues remain to be explored. In this work, the electrical analogues of different vehicle models are presented. A new and not previously reported analogy between inertial coupling and electrostatic capacitive coupling is found and described. Several examples are provided to highlight the benefits of this analogy. Well-known mechanical systems like the half-car or three three-axle vehicle models are discussed and some numerical results are presented. To the best of the author’s knowledge, such systems were never dealt with by using a full electromechanical analogy. The mechanical equations are also derived and compared with those of the electrical domain for harmonic steady-state analysis.

ТЕОРЕМА ОБ ИЗМЕНЕНИИ ЭНЕРГИЙ ПАРЦИАЛЬНЫХ ДВИЖЕНИЙ ГОЛОНОМНЫХ МЕХАНИЧЕСКИХ, ЭЛЕКТРИЧЕСКИХ И ЭЛЕКТРОМЕХАНИЧЕСКИХ СИСТЕМ С НЕСКОЛЬКИМИ СТЕПЕНЯМИ СВОБОДЫ

The purpose of this research is to formulate and prove the principle of energy of partial subsystems for mechanical, electrical, and electromechanical holonomic systems with time-independent constraints, as well as the development of a simple method to derive equations of motion for such systems. This principle is helpful in giving short courses of theoretical mechanics to students who know only the basic principle of energy and the D’Alembert principle. Two issues are covered in this paper: firstly, the formulation of the principle of energies for interacting mechanical partial subsystems, including the proof of the theorem, and, finally, the application of the developed method for mechanical, electrical, and electromechanical systems. The energy principle is developed using the D’Alembert principle for partial motions of the system when deriving kinetic and power balance equations. For electrical and electromechanical systems, the principle is based on the first electromechanical analogy of Maxwell’s postulate and Kirchhoff 's laws. As examples, the principle allowed obtaining equations of motion of mechanical systems with three degrees of freedom: rotation of a disk on an elastic shaft, dynamics of a vibration table, an electrical system with two cyclic currents connected through a resistor, and an electromechanical system of the acceleration sensor.