Dynamics and synchronization analysis of coupled fractional-order nonlinear electromechanical systems

A fractional-order (FO) nonlinear model is used to describe an electromechanical system. We make capital out of the fact that for realistic modeling, the electric characteristics of a capacitor include a fractional-order time derivative. The dynamics and synchronization of coupled fractional-order nonlinear electromechanical systems are analyzed. Detailed attention is granted to the bifurcations that can occur in the dynamics of a single uncoupled electromechanical system as the fractional-order varies. For example, the fractional-order counterparts of the chaotic 4-order system are periodic at orders less than 3.985. The effect of the fractional-order on the condition of occurrence of synchronization phenomena in the network of many mutually coupled fractional-order nonlinear electromechanical systems is analyzed, especially when they are chaotic. An insight on the overall dynamics of the network is provided. It is shown that the dynamics of both the uncoupled system and the network are very sensitive to changes in the order of the fractional derivative.     

Dynamics of the electromechanical sieve with hysteretic iron-core inductor

We study bifurcations and the chaotic behavior of a periodically forced electromechanical sieve. The dynamical behavior of the system is analyzed when supplied with the sinusoidal and square voltage sources. Analytical calculations and numerical simulations are also carried out for this electromechanical system and the results obtained are shown in terms of frequency–response diagrams, time–displacement diagrams, and phase portraits. Depending on the system parameters the analytical calculations and the numerical simulations exhibit regions of periodic and chaotic behaviors. For experimental validation, a small electromechanical sieve has been designed and realized. Amplitude jumps, hysteresis, and multistability are also observed. Good agreements are found between our theoretical results and experimental ones.

     

The principle of virtual work in mechanical and electromechanical systems

Summary The principle of virtual work is applied to electromechanical systems as the foundation of a unifying concept for modelling mechatronical systems. After the presentation of an important result in the field of mechanics, the expansion of the principle on electrical networks and electromechanical systems is shown. The use of the principle of virtual work in the domain of electromechanics yields an analogous form to the central equation of mechanics which is valid for holonomic and nonholonomic systems. The electrotechnical part of the system is confined to networks. The derivation of the mathematical model is demonstrated on the example of a simple electromechanical oscillation circuit. In addition, the physical systems are separately treated, taking into account the explicit constraints on the basis of the Lagrangian multiplier method.     

Nonlinear control in an electromechanical transducer with chaotic behaviour

The electromechanical transducer considered in this work is composed of a mechanical oscillator linked to an electronic circuit. Simulations results have determined that for some combination of parameters the electromechanical system is subject to chaotic motion with resonant transient behavior, and after the resonant transient the mechanical system (MS) synchronizes with the electrical system (ES). In order to improve the transient response, avoiding both the chaotic and resonant behaviors, a nonlinear control system is designed, a feedback control strategy is used to drive the system into the desired periodic orbit, and a nonlinear feedforward strategy is used to keep the system into the periodic orbit, obtained by the Fourier series. Two control techniques are used and compared, namely: the state dependent Ricatti equation and the optimal linear feedback control. Numerical simulations results are shown in order to compare the results, considering parametric uncertainties. Additionally, the energy transfer “pumping” between the ES and the MS is also analysed.     

Dynamics and control of a self-sustained electromechanical seismographs with time-varying stiffness

This paper is concerned with the nonlinear dynamics and vibration control of an electromechanical seismograph system with time-varying stiffness. The instrument consists of an electrical part coupled to mechanical one and is used to record the vibration during earthquakes. An active control method is applied to the system based on cubic velocity feedback. The electromechanical system is subjected to parametric and external excitations and modeled by a coupled nonlinear ordinary differential equations. The method of multiple scales is used to obtain approximate solutions and investigate the response of the system. The results of perturbation solution have been verified through numerical simulations, where different effects of the system parameters have been reported.     

Anti-plane time-harmonic Green's functions for a circular inhomogeneity in piezoelectric medium with a spring- or membrane-type interface

The present work focuses on the two-dimensional anti-plane time-harmonic dynamic Green's functions for a circular inhomogeneity immersed in an infinite matrix with an imperfect interface, where both the inhomogeneity and matrix are assumed to be piezoelectric and transversely isotropic. Two types of imperfect interface, the spring-type interface with electromechanical coupling and the membrane-type interface, are considered. The former type is often used to model the electromechanical damage along the interface while the latter is largely employed to simulate surface/interface effect of nano-sized inhomogeneity. By using the Bessel function expansions, explicit solutions for the electromechanical fields induced by a time-harmonic anti-plane line force and line charge located in an unbounded matrix as well as the circular inhomogeneity are respectively derived. The present solutions can recover the anti-plane Green's functions for some special cases, such as the dynamic or quasi-static Green's functions of piezoelectricity with perfect interface as well as the dynamic or quasi-static Green's functions of pure elasticity with imperfect interface. For detailed discussions, selected analytical results are presented. Dependence of the electromechanical fields on circular frequency as well as interface properties is examined. The size effect related to interfacial imperfection is also discussed.     

Dynamics of a cantilever arm actuated by a nonlinear electrical circuit

The idea in this paper is to present some analytical and numerical results on the investigation of the dynamics of a nonlinear electromechanical system including a cantilever robot arm manipulator, harmonically actuated through an electric circuit. We use the method of harmonic balance to derive oscillatory solutions. Forced vibrations are analyzed showing that numerical results are in agreement with those obtained analytically for the stationary response. The system presents various types of nonlinear behaviors including chaos.     

Application of the homotopy analysis method to nonlinear characteristics of a piezoelectric semiconductor fiber

Based on the nonlinear constitutive equation, a piezoelectric semiconductor(PSC) fiber under axial loads and Ohmic contact boundary conditions is investigated.The analytical solutions of electromechanical fields are derived by the homotopy analysis method(HAM), indicating that the HAM is efficient for the nonlinear analysis of PSC fibers, along with a rapid rate of convergence. Furthermore, the nonlinear characteristics of electromechanical fields are discussed through numerical results. It is shown that the asymmetrical distribution of electromechanical fields is obvious under a symmetrical load,and the piezoelectric effect is weakened by an applied electric field. With the increase in the initial carrier concentration, the electric potential decreases, and owing to the screening effect of electrons, the distribution of electromechanical fields tends to be symmetrical.     

磁力耦合道路能量收集设计与动力学分析

通过在交通环境布置无线传感器等小型机电系统, 实现交通状况监测、交通系统管控、交通设施健康状态监测等, 可以使交通系统更加安全、有序、高效地运行. 但是, 如何为这些广泛分布的小型机电系统供能？本文提出了一种磁力耦合道路能量收集设计, 用以收集车辆滚压能量并转换成电能. 通过磁力耦合进行无接触能量传递, 减小了装置受到的冲击并使得装置具有良好密封性, 从而提升装置的鲁棒性. 通过升频齿轮机构、棘轮机构将车辆滚压激励转换为高速单向旋转, 并且通过换向齿轮机构能够继续收集复位弹性势能, 提高了收集装置的输出功率. 基于磁力耦合道路能量收集系统的工作原理建立了机电耦合动力学模型. 数值仿真探究了减速带限位距离和复位弹簧刚度等关键设计参数对能量采集系统动力学和电学性能的影响. 能量采集系统在车速为50 km/h时最大输出电压为76.28 V, 最大功率为59.94 W. 磁力耦合道路能量收集装置可以成为未来智慧交通系统的重要组成部分, 俘获交通环境能量为交通环境中小型机电系统提供可持续的绿色无碳电力.      

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

This paper deals with problems for which it is necessary to represent the oscillations of the electromechanical seismograph about their position of equilibrium as regards the synchronous condition. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of the stable orbit with an unstable one. Then, global bifurcations and chaotic dynamics of an electromechanical seismograph are the aims of this study. The electrical part of the model is described by an extended force Rayleigh oscillator with Φ ⁶-potential, while the mechanical part is described by a damped and driven linear oscillator. By using the direct perturbation technique, we analytically obtain the general solution of the first-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos in the case where the Φ ⁶-potential is three wells, which are complemented by numerical simulations by which we illustrate the bifurcation curves and the fractality of the basins of attraction. The results show that the threshold amplitude of harmonic excitation for the onset of instability will move upwards as the amplitude intensity of the ground motion increases. These results suggest that much attention should be paid to controlling the increase of the amplitude of the ground motion, especially when the harmonic excited electromechanical seismograph system as a main device is applied to some practical systems.     

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

In this paper, we investigated the effectiveness of the linear electromechanical vibration absorber (LEVA) and a nonlinear electromechanical vibration absorber (NEVA) in the vibration attenuation for nonideal structures (NIS). This electromechanical damping device consists of an electrical system coupled magnetically to a mechanical structure under a nonideal excitation. An analysis of the effects of the parameters of coupling and of nonlinear coefficients with increasing of constant torque of the DC motor is presented.     

层合结构压电器件的机电耦合响应

压电传感嚣和致动器都可以看成是由压电材料层和非压电(弹性)材料层交替铺设而成。对于这类任意铺设的层合板悬臂梁结构,推导出了表示力学变形与外加电场之间耦合效应的解析表达式。进而,又推导出了两类(一类为单层压电-弹性层。另一类为双层压电-弹性层)层合型悬臂梁结构机电耦合性能的解析公式。在该机电耦合模型中,包括了两个压电常数d211和d222。最后。通过比较解析解、实验值以及有限元计算结果,发现它们吻合得很好。     

A coupled electromechanical analysis of a piezoelectric layer bonded to an elastic substrate: Part II,numerical solution and applications

This two-part contribution presents a novel and efficient method to analyze the two-dimensional (2-D) electromechanical fields of a piezoelectric layer bonded to an elastic substrate, which takes into account the fully coupled electric and mechanical behaviors. In Part I, we have obtained a system of governing integro-differential equations for the structure via a variational principle. This part presents a numerical solution algorithm of the integro-differential equations and the numerical results of some applications. A numerical algorithm for solving the system of four integro-differential equations with strongly singular kernels is developed. The convergence of the numerical algorithm is discussed. The numerical results suggest that the fully coupled electromechanical analysis is helpful for a better understanding of the performance of the piezoelectric sensor and actuator. The interfacial normal stress is much higher than the interfacial shear stress, suggesting that the interfacial normal stress causes a delamination initiation.     

层合结构压电器件的机电耦合效应

压电传感器和致动器都可以看成是一种复合材料层合板结构，由压电材料层和非压电(弹性)材料层交替铺设而成。对于这类任意铺设的层合板悬臂梁结构，我们推导出了表示力学变形与外加电场之间耦合效应的解析表达式。进而，又推导出了两类(一类为单层压电-弹性层，另一类为双层压电-弹性层)层合型悬臂梁结构机电耦合性能的解析公式。在该机电耦合模型中，包括了两个压电常数d211和d222。此外，还建立了含压电材料的有限元算式，进行了实验测量。最后，通过比较解析解(包括考虑了d222参数的理论值和没有考虑d222参数的理论值)，实验值以及有限元计算结果，发现它们吻合得很好，而且考虑d222是十分必要的。     

RATE DEPENDENT STRESS-STRETCH RELATION OF DIELECTRIC ELASTOMERS SUBJECTED TO PURE SHEAR LIKE LOADING AND ELECTRIC FIELD

The performance of dielectric elastomer(DE) transducers is significantly affected by viscoelastic relaxation-induced electromechanical dissipations.This paper presents an experimental study to obtain the rate dependent stress-stretch relation of DE membranes(VHB TM 9473) subjected to pure shear like loading and electric loading simultaneously.Stretching rate dependent behavior is observed.The results also show that the tensile force decreases as the voltage increases.The observations are compared with predictions by a viscoelastic model of DE.This experiment may be used for further studies of dynamic electromechanical coupling properties of DEs.     

电动机-弹性连杆机构系统的动态方程及其响应

针对三相交流电机转子振动偏心时不均匀气隙的气隙磁场,分析其实际运行状态的机电耦合关系．建立以电机横振、扭振为节点位移的电机单元,应用有限单元法建立含电机电磁参数和弹性连杆机构结构参数的系统动态方程,并根据该方程对系统的动态响应进行仿真计算和分析,且通过实验进行验征,表明所建方程较好地反映丁系统动态性能与其电磁参数、结构参数之间的关系．     

Piezoelectric Study on Elliptic Inhomogeneity Problem Using Alternating Technique

This paper presents a novel efficient procedure to analyze the elliptical inhomogeneity problem in piezoelectric materials under electromechanical loadings. The electromechanical loadings considered in this paper include a point force and a point charge or a far-field anti-plane shear and in-plane electric field. The analytical continuation method together with alternating technique is used to derive the electroelastic fields in terms of the corresponding homogeneous solution. Compared to existing related papers, this approach could lead to some interesting simplifications in solution procedure and the derived analytical solution for singularity problems can be employed as a Green's function to investigate matrix cracking in the inclusion/matrix system. Numerical results are provided to show the effect of the material mismatch, the aspect ratio and the loading condition on the electroelastic field due to the presence of the inhomogeneity.     

Dynamic characteristic analysis for clutch engagement process of series–parallel hybrid electric vehicle

Variable driving conditions can cause an integrated starter generator hybrid powertrain to switch between multiple drive modes. The addition of a permanent magnet synchronous motor (PMSM) gives hybrid powertrains complex electromechanical coupling characteristics. The effects of excitation sources, such as the engine and PMSM, may cause unstable behavior in the drive system, such as speed fluctuations during mode switches due to electromechanical coupling characteristics. Although traditional mode switch strategies and methods have achieved measurable results, they are difficult to improve. To solve this problem, we first considered the combination and separation of the clutch and establish a nonlinear model of mode switches for series–parallel hybrid electric vehicles. Then, we predicted the instability boundary of the drive system during mode switches. Experimental results indicated that the proposed instability boundary has higher accuracy. Numerical results showed that the three-mode switches have different thresholds of instability for the clutch structure gap. The decrease in electromagnetic torque and the increase in load excitation amplitude will improve the critical value of the clutch structure gap. The increase in load excitation frequency causes the critical value of the clutch structure gap to drop first and then rise.

     

Dynamics, chaos and synchronization of self-sustained electromechanical systems with clamped-free flexible arm

An electromechanical system with flexible arm is considered. The mechanical part is a linear flexible beam and the electrical part is a nonlinear self-sustained oscillator. Oscillatory solutions are obtained using an averaging method. Chaotic behavior is studied via the Lyapunov exponent. The synchronization of regular and chaotic states of two such devices is discussed and the stability boundaries for the synchronization process are derived using the Floquet theory. We compare the results obtained from a finite difference simulation to those from the classical modal approach.     

Dimensional reduction of a piezoelectric composite rod

In the present paper, a new generalized Timoshenko model is constructed for a composite rod with embedded or attached piezoelectric materials. This model is applicable to composite rods without prescribed electric potential along the lateral surfaces. The Variational-Asymptotic Method (VAM) is applied as a mathematical tool to carry out the dimensional reduction process. The present reduced model captured the effects of dielectric as well as the polarization of the piezoelectric material, which justifies its coupled electromechanical nature. First, the three-dimensional electromechanical enthalpy is asymptotically approximated by VAM using the slenderness of the rod as the small parameter and subsequently an equivalent one-dimensional electromechanical enthalpy is developed. Energy terms, which are asymptotically correct up to the second order are kept in the approximate enthalpy expression. For engineering applications, the approximate enthalpy is then transformed into a generalized Timoshenko model which has the traditional six mechanical degrees of freedom along with an extra one-dimensional electric degree of freedom.