自组装静电驱动微机电系统倾斜镜

研制了一种基于自组装技术的静电驱动微机电系统(MEMS)倾斜镜,并利用表面硅工艺PolyMUMPs制备了样品。倾斜镜主要由一个中心镜面,两个偏转梁和两个可实现自组装的复合悬臂梁组成。中心镜面离衬底的高度可通过增大金和多晶硅复合悬臂梁的残余应力梯度得到提升。热退火技术被用于提高金层的残余应力。器件结构利用有限元仿真软件进行了优化并通过实验进行了验证。经过200 ℃热退火后,倾斜镜的偏转角度可以达到3.6。该倾斜镜可运用于微光机电系统。     

A general closed-form solution for the static pull-in voltages of electrostatically actuated MEMS/NEMS

In this article, an analytical method for calculating pull-in voltage is proposed. This method can accurately predict pull-in voltage of clamped-free, clamped-clamped and curved micro- and nano-beams. In this study, mid-plane stretching, axial stress, initial deformation and the effect of size are taken into account. To achieve this goal, governing equation of beam based on modified couple stress theory was first derived and then transformed to a single degree of freedom (D.O.F) model by Galerkin method. In this model, electrostatic force appears in integral form which is approximated to non-integral form employing Genetic Algorithm. This single degree of freedom model provides means for obtaining critical deflection of beam and is used to find the general closed-form expression for pull-in voltage. The validation of the method was carried out by comparing the results with the existing literature.     

Application of an electrostatically actuated cantilevered carbon nanotube with an attached mass as a bio-mass sensor

In the present paper, another latent capability of SWCNT as a mass sensor is investigated. The relationship between the resonant frequency, dynamic pull-in voltage at the resonance frequency shift, and the attached mass is established by using the nonlocal Euler–Bernoulli beam theory. Using this relationship, a general closed-form nonlinear sensor-equation has been derived for the detection of the mass attached to the SWCNT. The aim of this study and present model is to show the sensitivity of the Cantilevered SWCNT to the values and positions of attached mass. Moreover, the results indicate that by increasing the value of attached mass and considering a single non-local scaling parameter (e₀), the values of dynamic pull-in voltage at the resonance frequency shift are decreased. Because of the small scaling parameter (e₀), the mass sensitivity of carbon nanotube increases, when the position of the attached mass is in the tip of a Cantilevered SWCNT length. The authority and the accuracy of these formulas are examined with other pull-in sensor equations in literatures. The results demonstrate that the new sensor equation can be applied for CNT-based mass sensors with rational accuracy.     

Multiple internal resonances in MEMS arch resonators

Micromachined shallow arch resonant beams have attracted significant attention thanks to their rich dynamical behavior, inherent nonlinearities, and the potential to excite various internal resonances. Currently, there is a lack of comprehensive experimental studies for the various types of internal resonances in arches and particularly at the micro and nano scales. Here, we aim to investigate and identify different types of internal resonances of an initially curved beam, electrothermally actuated and electrostatically driven, by electrical characterization techniques. Upon changing the electrothermal voltage of silicon micromachined arches, the second symmetric natural frequency of an arch is adjusted to near twice, three times, and four times the fundamental natural frequency, which gives rise to 2:1, 3:1, and 4:1 autoparametric resonances between the two modes. These resonances are demonstrated experimentally. We show various frequency-response curves of the total response around the excitation frequency and highlight the contribution of each mode before, during, and after the internal resonances. Allan-deviation results are also shown indicating enhanced frequency stabilization of the arch oscillation when experiencing internal resonances. These studies motivate further research in this direction to exploit internal resonances of micromachined resonators for practical applications, such as sensors and mechanical amplifier.     

An iterative method for nonlinear dynamical system of an electrostatically actuated micro-cantilever

This study proposes an iterative method, in which all iterations are linear, for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. The presented method is further improved, so that the CPU time needed is significantly reduced. This method provides solutions in excellent agreement with numerical ones.     

Optimization of concentric array resonators for wide band noise reduction

In air duct noise control, Helmholtz resonators (HR) are considered as narrow band attenuators. For some applications they can be combined in line to form a wide band silencer. This study investigates the role of distance between HR side branch openings on the whole array attenuation. In the case of two resonators with same performance, the optimal distance can be calculated and corresponds to the quarter wave of HR mean frequency. On three or more HR arrays, relationships between resonators parameters and optimal lengths are much more complex. Tuning of such a device requires taking many geometrically coupled parameters into account; hence, design has to be automated. To operate this process, a 2D FEM COMSOL model has been coupled to a global MATLAB optimization solver. Among different types of constructions, arrays made of concentric resonators with transversal openings offers the most efficient and flexible design to optimize distance between openings. This methodology was applied to an existing turbo compressor silencer. Modifying openings and chambers arrangement, using the proposed approach increased the attenuation band by 10%. Another application concerning an air box for a two stroke engine was also investigated. This resulted in a 16L two chambers concept, being replaced by a more compact and more efficient, 8.3L wide band silencer, made of 8 resonators. With this approach it therefore becomes possible to handle available space and required noise attenuation on a required frequency band, all in one process.     

Deterministic chaos and natural phenomena

The natural time seriesf ₀ F ₂, F10.7, and AE are analyzed and low-dimensional attractors are found, characterized by the correlation dimension and the lower bound of the Kolmogorov entropy. Sources of noise in natural time series are discussed and the concept of extended systems is introduced and used to explain why the number of data required to calculate the correlation dimension of natural time series is higher than that reported by other authors.     

Numerical model for the calculation of the electrostatic force in non-parallel electrodes for MEMS applications

In this paper, we investigate the electrical behavior of an electrostatic actuator made of a non-parallel plate's electrodes configuration. The resultant actuation force is caused by the asymmetry of the subsequent electric fringing-fields. This is designed due to the out-of-plane asymmetry of a non-stationary electrode and its two sides actuating stationary electrodes. The electrostatic force is numerically calculated through the results of a two-dimensional numerical solution of the electrostatic problem using Finite-Element Method (FEM). The main objective in this work is to examine the influence of the design parameters on the actuating resultant electrostatic force in this particular arrangement. Four key design parameters were examined: the width and thickness of the electrodes (movable and stationary) as well as the lateral and vertical separation distances between the movable and grounded electrodes. We found out, through several simulations, that both lateral and vertical offsets as well as the electrodes thickness are significant factors in the optimization of the performance of the actuator in such configuration, while the performance seemed to be independent of the electrodes widths. The resultant actuating force level increased with increasing the electrode thickness and with decreasing the electrodes lateral separation distance.     

Noise-induced bifurcations and chaos in the average motion of globally-coupled oscillators

A system of coupled master equations simplified from a model of noise-driven globally coupled bistable oscillators under periodic forcing is investigated. In the thermodynamic limit, the system is reduced to a set of two coupled differential equations. Rich bifurcations to subharmonics and chaotic motions are found. This behavior can be found only for certain intermediate noise intensities. Noise with intensities which are too small or too large will certainly spoil the bifurcations. In a system with large though finite size, the bifurcations to chaos induced by noise can still be detected to a certain degree. Received 6 April 1999 and Received in final form 1 November 1999     

Signal synchronous transmission of current-modulated semiconductor laser under bounded noise

The synchronous transmission problem of chaotic signal between current-modulated semiconductor lasers is investigated using variable coupling method. The theoretical analysis about characteristics of current-modulated semiconductor lasers is derived. According to Lyapunov theory, the condition which can realize synchronous transmission between semiconductor lasers is derived through determining maximum Lyapunov exponent of the coupling system. Further study the synchronization performance between semiconductor lasers under the influence of bounded noise, the results show that it has a strong anti-interference ability.     

Variable optical attenuator based on a vertical comb drive actuated MEMS micromirror

This letter presents the design, simulation, fabrication, and successful demonstration of a variable optical attenuator (VOA) based on a micromachined micromirror combined with an optical fiber collimator. The micromirror has a size of 500 μm in diameter and a rotational resonance of 4.94 kHz. The micromirror was actuated by vertical comb drive which was fabricated by bulk micromachining process on a silicon on insulator (SOI) wafer. The VOA operates at a low driving voltage of 4.4 V corresponding to the rotation angle of 0.3°. The turn-on and turn-off response time of the VOA are 1.6 ms and 2.74 ms, respectively. Finally, the optical attenuation was measured and an optical attenuation as large as 40 dB was obtained.     

Dynamic maps in phase-conjugated optical resonators

In this article the dynamical behavior of a beam within a ring-phase-conjugated resonator is modeled using two-dimensional iterative maps. In particular and as an example it is explicitly shown how the difference equations of the Duffing map can be used to describe the dynamic behavior of what we call Duffing beams i.e. beams that behave according to the Duffing map. The matrix of a Duffing map generating device is found in terms of the Duffing parameters, the state variables and the resonator parameters. To our knowledge this is the first time that the mathematical characteristics of an optical device in an optical cavity are stated so that a Duffing map is obtained as the dynamics for the ray beams.     

Noise-induced synchronization of spatiotemporal chaos in the Ginzburg-Landau equation

We have studied noise-induced synchronization in a distributed autooscillatory system described by the Ginzburg-Landau equations, which occur in a regime of chaotic spatiotemporal oscillations. A new regime of synchronous behavior, called incomplete noise-induced synchronization (INIS), is revealed, which can arise only in spatially distributed systems. The mechanism leading to the development of INIS in a distributed medium under the action of a distributed source of noise is analytically described. Good coincidence of analytical and numerical results is demonstrated.     

Coherence effect on decryption characteristics in message modulation type chaos secure communication systems using fiber-optic ring resonators

We numerically investigated the dependence of the decryption characteristics in a message modulation type chaos secure communication system using optical fiber ring resonators (OFRRs) on the coherence condition of carrier light. Since the output dynamics of OFRRs were formed on the basis of interference phenomenon among the circulated components in OFRRs, the coherence condition of input light affected inherently the OFRR output dynamics, resulting in the decryption characteristics. It was found that the decryption characteristics degraded as coherence length increased, i.e., as the spectral width of the input light decreased. The decryption characteristics also grew worse as the parameter differences between the transmitter and the receiver became larger.     

非稳腔模式计算中Colins公式适用性的分析

Ｃｏｌｉｎｓ公式将几何光学和波动光学联系在一起，能以简单的形式描述相干光在复杂光学系统中的传输，但忽略了光学系统中一些光学元件的衍射损耗。当Ｃｏｌｉｎｓ公式用于激光谐振腔的本征模式计算时，其适用程度与被忽略腔镜的有效菲涅尔数有关。本文用数值方法求解了两组谐振腔本征积分方程，一组应用Ｃｏｌｉｎｓ公司推导，另一组用菲涅尔－惠更斯衍射积分推导，结果表明：对稳定腔Ｃｏｌｉｎｓ公式基本适用；对非稳腔，当被忽略腔镜的有效菲涅尔数＞１时，原则上可以用，当被忽略腔镜的有效菲涅尔数＜１时不适用；对有源非稳腔基本适用。     

The dynamics of exchange rate time series and the chaos game

This work presents a novel method of reconstructing some relevant characteristics of exchange rate time series by the superposition of two components: a mostly deterministic one, the chaos game as expressed by the Yuan/USD exchange rate and a purely stochastic one, Gaussian white noise. We analyzed 20 economic systems with the average Index of Economic Freedom above 50. The considered characteristics (the Lempel-Ziv complexity index, the slimness of the distribution and the Iterated Function Systems clumpiness test) are well reproduced by the reconstruction process. Additional confirmation is obtained by an analysis of the exchange rate of the Romanian national currency as an example of an application of the method to a transition economy, and by an analysis of the time series of the Euro-zone as an example of an application to a multinational system using a shorter time series.     

Noise-induced Hopf-bifurcation-type sequence and transition to chaos in the lorenz equations

We study the effects of noise on the Lorenz equations in the parameter regime admitting two stable fixed point solutions and a strange attractor. We show that noise annihilates the two stable fixed point attractors and evicts a Hopf-bifurcation-like sequence and transition to chaos. The noise-induced oscillatory motions have very well defined period and amplitude, and this phenomenon is similar to stochastic resonance, but without a weak periodic forcing. When the noise level exceeds certain threshold value but is not too strong, the noise-induced signals enable an objective computation of the largest positive Lyapunov exponent, which characterize the signals to be truly chaotic.     

Angular spectrum theory to calculate coupling efficiency in rectangular waveguide resonators

Coupling efficiency of the rectangular waveguide resonators are discussed in terms of the method of angular spectrum theory. Under the condition given in the paper, the coupling coefficients for the EH₁₁ mode in the rectangular waveguide resonator are presented as a function of mirror curvature and position. It is shown that there exist two special geometries to provide low coupling efficiency. The method can be applied to the other modes.     

Surface vibrational modes in disk-shaped resonators

The natural frequencies and distributions of displacement components for the surface vibrational modes in thin isotropic elastic disks are calculated. In particular, the research is focused on even solutions for low-lying resonant vibrations with large angular wave numbers. Several families of modes are found which are interpreted as modified surface modes of an infinitely long cylinder and Lamb modes of a plate. The results of calculation are compared with the results of the experimental measurements of vibrational modes generated by means of resonant excitation in duraluminum disk with radius of ≈90 mm and thickness of 16 mm in the frequency range of 130–200 kHz. An excellent agreement between the calculated and measured frequencies is found. Measurements of the structure of the resonant peaks show splitting of some modes. About a half of the measured modes has splitting Δ_fsplit/_fmode$\mathrm{\Delta }{f}_{\mathrm{split}}/f_{\mathrm{mode}}$ at the level of the order of 10⁻⁵. The Q-factors of all modes measured in vacuum lie in the interval (2…3) × 10⁵. This value is typical for duraluminum mechanical resonators in the ultrasonic frequency range.     

Effects of electrodes with continuously varying thickness on energy trapping in thickness-shear mode quartz resonators

We study the effects of electrodes of nonuniform thickness on thickness-shear vibration frequencies and mode shapes of quartz resonators. This paper extends a previous paper from electrodes of stepped thickness to continuously varying thickness. Numerical results for electrodes of linearly varying thickness are presented. The results show that strong energy trapping can be achieved and adjusted using electrodes with variable thickness.