Generation of Chaotic Beats in a Modified Chua's Circuit Part I: Dynamic Behaviour

This paper and the companion one [Cafagna, D. and Grassi, G., Nonlinear Dynamics, this issue] present the new phenomenon of chaotic beats in non-autonomous Chua's circuit, driven by two sinusoidal inputs with slightly different frequencies. In particular, in this paper the behaviour of the proposed circuit is analyzed both in time-domain and state-space, confirming the chaotic nature of the phenomenon and the effectiveness of the design.     

Topological Invariants in a Model of a Time-Delayed Chua's Circuit

In the last 30 years, some authors have been studying several classes of boundary value problems (BVP) for partial differential equations (PDE) using the method of reduction to obtain a difference equation with continuous argument which behavior is determined by the iteration of a one-dimensional (1D) map (see, for example, Romanenko, E. Yu. and Sharkovsky, A. N., International Journal of Bifurcation and Chaos 9(7), 1999, 1285–1306; Sharkovsky, A. N., International Journal of Bifurcation and Chaos 5(5), 1995, 1419–1425; Sharkovsky, A. N., Analysis Mathematica Sil 13, 1999, 243–255; Sharkovsky, A. N., in “New Progress in Difference Equations”, Proceedings of the ICDEA'2001, Taylor and Francis, 2003, pp. 3–22; Sharkovsky, A. N., Deregel, Ph., and Chua, L. O., International Journal of Bifurcation and Chaos 5(5), 1995, 1283–1302; Sharkovsky, A. N., Maistrenko, Yu. L., and Romanenko, E. Yu., Difference Equations and Their Applications, Kluwer, Dordrecht, 1993.). In this paper we consider the time-delayed Chua's circuit introduced in (Sharkovsky, A. N., International Journal of Bifurcation and Chaos 4(5), 1994, 303–309; Sharkovsky, A. N., Maistrenko, Yu. L., Deregel, Ph., and Chua, L. O., Journal of Circuits, Systems and Computers 3(2), 1993, 645–668.) which behavior is determined by properties of one-dimensional map, see Sharkovsky, A. N., Deregel, Ph., and Chua, L. O., International Journal of Bifurcation and Chaos 5(5), 1995, 1283–1302; Maistrenko, Yu. L., Maistrenko, V. L., Vikul, S. I., and Chua, L. O., International Journal of Bifurcation and Chaos 5(3), 1995, 653–671; Sharkovsky, A. N., International Journal of Bifurcation and Chaos 4(5), 1994, 303–309; Sharkovsky, A. N., Maistrenko, Yu. L., Deregel, Ph., and Chua, L. O., Journal of Circuits, Systems and Computers 3(2), 1993, 645–668. To characterize the time-evolution of these circuits we can compute the topological entropy and to distinguish systems with equal topological entropy we introduce a second topological invariant.     

光纤陀螺高速检测电路设计

缩短光纤长度是光纤陀螺降低成本、实现小型化的重要手段，中介绍了一种适用于短光纤的光纤陀螺高速检测电路，并针对高速检测电路的几项关键技术进行了讨论。测试结果表明：高速检测电路比普通检测电路具有更高的性能，其应用于短光纤陀螺的方案是可行的。     

静电陀螺转子位移测量电路的研究

—静电陀螺转子位移测量电路是静电陀螺支承系统的重要部件。它直接影响转子在电极球腔中的失中度，从而导致陀螺漂移。因此在温度变化及电磁干扰情况下，必须提高测量电路的分辨率和零位稳定性。本文在理论分析和实验研究的基础上，提出参数优化设计方法和模块化结构设计。实验结果表明所研制的电路性能良好，工作稳定度达到了高精度静电陀螺仪的要求。     

大量程石英加速度计二元调宽再平衡回路的设计与应用

二元调宽再平衡回路具有施矩功率恒定，转换精度高，易于同计算机通讯等一系列优点，因而在惯性元件伺服回路中得到广泛应用。中介绍了二元调宽再平衡回路在大量程石英加速度计线路上的应用，通过理论设计和试验，选择合理电参数，并取得了满意的结果。     

新型断路器操作机构的力学测试

为了实现一种结构简单、成本低廉、耗能较低的高压断路器的操作机构,在分析典型永磁电动操作机构的基础上,提出了一种采用永磁驱动的新型操作机构。利用MTS809材料试验系统测得断路器真空室的触头反力,使用Maxwell软件对断路器操作机构的磁力进行仿真与优化。在此基础上,确定操作机构的整体结构并做出10kV真空断路器原理样机。再利用MTS809系统对原理样机的驱动力进行测试验证。驱动力测试结果表明,新型永磁驱动操作机构原理可行,10kV真空断路器原理样机达到预期的设计目标。     

Subharmonic oscillations in three-phase circuits

This paper analyzes the subharmonic oscillations generated in three-phase circuits by the asymptotic method. As the result of the analysis, we find that there are three kinds of the 1/3-harmonic oscillations, 1/3-harmonic oscillation with beats, 1/3-harmonic oscillation without beats and 1/3-harmonic oscillation occurring in a single phase of the three-phase circuit. By means of an experimental circuit we confirm these oscillations.     

A Chaotic Circuit with Ferroelectric Nonlinearity

In this paper, the possibility of observing strange attractors in an electronic circuit including a nonlinear ferroelectric component has been investigated. The ferroelectric constitutes the medium interposed between the two plates of a capacitor. A circuit including the nonlinearity of the ferroelectric has been designed, while the parameters have been found by performing numerical integration with respect to different values of them. The circuit has been realized on a discrete components board. Experimental results, showing that for a suitable range of parameters a chaotic attractor emerges, are reported.     

Circuit implementation of a piezoelectric buckled beam and its response under fractional components considerations

In this paper, an analog testing circuit and determinist averaging method for a vibration energy harvesting system with fractional derivative and nonlinear damping under a sinusoidal vibration source is proposed in order to predict the system response and its stability. The objective of this paper is to show that there is a possibility to make a pre-experimental design of the structure by using analog circuit and discussing the performance of a system with fractional derivative. Bifurcation diagram, poincaré maps and power spectral density are provided to deeply characterize the dynamic of the system. These results are corroborated by using 0–1 test. By using the Melnikov method, we find the necessary condition for which homoclinic bifurcation occurs. Understanding and predicting this bifurcation is very judicious in the energy harvesting field because it may lead to different types of motion in the perturbed system. The appearance of chaotic vibrations increases the frequency’s bandwidth of the harvester thereby, allowing to harvest more energy. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim^®). The corresponding electronic circuit is designed exhibiting transient to chaos in accord with numerical simulations. The impact of fractional derivatives is presented upon the power generated by the system. In addition, by combining the harmonic force and a random excitation, the stochastic resonance appears, giving rise to large amplitude of vibration and consequently, enhancing the performance of the system. The results obtained in this work show the interest of using the electronic circuit to make the experiment analysis of the physical structure and also, the effects of the use of piezoelectric material exhibiting fractional properties in this research field.     

微喷射物质作用下脉冲信号电探针的放电机理

针对脉冲信号电探针在微喷射物质作用下出现的“非正常”放电现象,提出了微喷射物质K+R_x等效电路模型,用以解释微喷射物质导通电探针放电机理。开展爆轰实验,联合X射线测试技术,确定了电探针放电区域处于微喷射区与微层裂区的过渡地带,并发现电探针的3类“非正常”放电现象。建立电路仿真模型,将微喷射物质等效成K+R_x电路,调节K+R_x等效电路模型参数,模拟电探针的3类“非正常”放电现象。仿真结果表明,K+R_x等效电路模型很好地解释了微喷射物质作用下脉冲信号电探针的放电机理。     

提高石英音叉陀螺驱动信号稳定性的数字电路设计

石英音叉陀螺通常采用模拟解调电路,现有模拟电路驱动电路幅度稳定性不高,限制了石英音叉陀螺整机性能,可以采用数字电路提高驱动幅度稳定性。文中先讨论了驱动信号幅度影响石英音叉陀螺性能的原因;然后设计了数字电路,采用数字信号处理算法实现了数字电路闭环驱动,并对数字电路闭环驱动的自动增益控制误差进行了分析;最后,对模拟电路和数字电路的驱动幅度稳定性进行了对比测试,定温情况下,模拟电路驱动幅度稳定性的均方差为4.77×10-4V,数字电路的幅度稳定性的均方差达到8.26×10-5V,模拟电路幅度稳定性在全温范围的均方差为0.0680 V,数字电路的均方差仅为0.0006V。实验表明,数字电路的驱动信号幅度稳定性显著提高。     

相似电路耦合模型及其在压电—梁结构分析中的应用

根据线性系统微分方程的相拟性确定机械系统的相似电路,由压电材料的本构和动力方法确定压电材料作为电耦合的变压器,从而用一具耦合的电路系统模拟智能结构的电学和力学行为,通过一个压电－梁智能结构的分析,证明了模型的可用性。     

高精度加速度计A/D转换电路的温漂补偿

从理论上分析了温度变化对高分辨率A/D转换芯片输出的影响,通过静态试验建立了加速度计输出与A/D转换电路温漂之间的关系,并依照这种关系对加速度计输出进行了补偿,补偿后加速度计输出精度得到了明显提高。     

自抗扰控制思想在动力调谐陀螺仪力平衡回路中的应用

提出了动力调谐陀螺力平衡回路的自抗扰控制方法(ADRC)。在计算机仿真的基础上搭建陀螺仪力平衡回路硬件电路，利用转台对动力调谐陀螺施加不同扰动，观察在大角度或大角速率等动态条件下ADRC控制技术对陀螺仪的控制效果。     

高g值冲击下存储测试电路模块缓冲保护研究

为了采用弹载存储测试技术记录弹体高速侵彻硬目标过程中的加速度—时间曲线,必须对存储测试电路模块进行缓冲保护。本文利用非线性缓冲理论、技术,选择较理想的缓冲材料,设计出缓冲器件-泡沫铝试件,进行了静态压缩,得到应力-应变曲线,采用LS-DYNA模拟了空气炮冲击实验中泡沫铝试件的缓冲效果,并对应用于某型号弹侵彻混凝土靶的存储测试电路模块进行了缓冲保护,提高了数据的捕获率和电路模块的重复使用次数。通过试验证明了所设计缓冲器件对电路模块具有保护效果。     

COUPLED ANALYSIS FOR THE HARVESTING STRUCTURE AND THE MODULATING CIRCUIT IN A PIEZOELECTRIC BIMORPH ENERGY HARVESTER

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio （length/thickness） and the non-dimensional end mass of the harvesting structure. The numerical results show that： （1） the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and （2） for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.     

Temperature field analysis of IC molding process based on three dimensional finite element model

In the case presented in this paper, the distribution of temperature fields of the molding model during each time interval was obtained as the simulation proceeded along the molding time by using the 3D FEM with a simple division mesh. The simulation results indicate that the most temperature rise is located at the upper right hand corner of the die pad, while the least temperature rise during the molding process is located at the upper right hand corner of the lead frame. Based on the simulation results of the temperature field distribution in the molding model, we obtained the temperature variation trend as a result of changes in the geometric shapes of the molding model. Therefore, the information on the molding model and the analysis of temperature distribution during the integrated circuit molding process presented in this paper can be considered as references for the molding design for integrated circuit packaging process.     

Periodic orbits,basins of attraction and chaotic beats in two coupled Kerr oscillators

Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect, i.e., interaction of optical waves with nonlinear medium with polarizability χ ⁽³⁾ is the basic phenomenon needed to explain, for example, the process of light transmission in fibers and optical couplers. In this paper, we analyze the two Kerr oscillators coupler and we show that there is a possibility to control the dynamics of this system, especially by switching its dynamics from periodic to chaotic motion and vice versa. Moreover, the switching between two different stable periodic states is investigated. The stability of the system is described by the so-called maps of Lyapunov exponents in parametric spaces. Comparison of basins of attractions between two Kerr couplers and a single Kerr system is also presented.     

Effect of electric boundary conditions on crack propagation in ferroelectric ceramics

In this paper, the effect of electric boundary conditions on Mode I crack propagation in ferroelectric ceramics is studied by using both linear and nonlinear piezoelectric fracture mechanics. In linear analysis, impermeable cracks under open circuit and short circuit are analyzed using the Stroh formalism and a rescaling method. It is shown that the energy release rate in short circuit is larger than that in open circuit. In nonlinear analysis, permeable crack conditions are used and the nonlinear effect of domain switching near a crack tip is considered using an energy-based switching criterion proposed by Hwang et al.（Acta Metal. Mater.,1995）. In open circuit, a large depolarization field induced by domain switching makes switching much more diffcult than that in short circuit. Analysis shows that the energy release rate in short circuit is still larger than that in open circuit, and is also larger than the linear result. Consequently,whether using linear or nonlinear fracture analysis, a crack is found easier to propagate in short circuit than in open circuit, which is consistent with the experimental observations of Kounga Njiwa et al.（Eng. Fract. Mech., 2006）.     

动力调谐陀螺动基座启动再平衡电路

—本文详细介绍了动力调谐陀螺动基座启动再平衡电路的设计原因、设计思路和方法，达到的效果以及适用范围等。