Inhomogeneous deformations and pull-in instability in electroactive polymeric films

By means of a bifurcation analysis we show the onset of inhomogeneous equilibrium configurations in thin electroelastic polymeric films under assigned voltage. The resulting activation threshold decreases the diffusely adopted value obtained under the assumption of homogeneous deformations. We argue that the bifurcated inhomogeneous solution describes experimentally observed localization effects.     

Lateral pull-in instability of electrostatic MEMS transducers employing repulsive force

Nonlinear Dynamics - We report on the lateral pull-in in capacitive MEMS transducers that employ a repulsive electrostatic force. The moving element in this system undergoes motion in two...     

Size-dependent dynamic pull-in instability of hydrostatically and electrostatically actuated circular microplates

In the present study, the dynamic pull-in instability and free vibration of circular microplates subjected to combined hydrostatic and electrostatic forces are investigated. To take size effects into account, the strain gradient elasticity theory is incorporated into the Kirchhoff plate theory to develop a nonclassical plate model including three internal material length scale parameters. By using Hamilton’s principle, the higher-order governing equation and the corresponding boundary conditions are obtained. Afterward, a generalized differential quadrature (GDQ) method is employed to discritize the governing differential equations along with simply supported and clamped edge supports. To evaluate the pull-in voltage and vibration frequencies of actuated microplates, the hydrostatic-electrostatic actuation is assumed to be calculated by neglecting the fringing field effects and utilizing the parallel plate approximation. Also, a comparison between the pull-in voltages predicted by the strain gradient theory and the degenerated ones is presented. It is revealed that increasing the dimensionless internal length scale parameter or decreasing the applied hydrostatic pressures leads to higher values of the pull-in voltage. Moreover, it is found that the value of pull-in hydrostatic pressure decreases corresponding to higher dimensionless internal length scale parameters and applied voltages.     

Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures

The dynamic pull-in instability of double clamped microscale beams actuated by a suddenly applied distributed electrostatic force and subjected to non-linear squeeze film damping is investigated. A reduced order model is built using the Galerkin decomposition with undamped linear modes as base functions and verified through comparison with numerical finite differences solution. The stability analysis of a beam actuated by one and two electrodes symmetrically located at two sides of the beam and operated by a step-input voltage is performed by evaluating the largest Lyapunov exponent, the sign of which defines the character of the response. It is shown that this approach provides an efficient quantitative criterion for the evaluation of dynamic pull-in instability, especially when combined with compact reduced order models. Based on the Lyapunov exponent criterion, the influence of various parameters on the beam dynamic stability is investigated.     

Application of homotopy analysis method in studying dynamic pull-in instability of microsystems

In this study, homotopy analysis method is used to derive analytic solutions to predict dynamic pull-in instability of electrostatically-actuated microsystems. The model considers midplane stretching, initial stress, distributed electrostatic force and fringing fields effect. Influences of different parameters on dynamic pull-in instability are investigated. Results are in good agreement with numerical and experimental findings.     

Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces

In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under the combined effects of electrostatic and intermolecular forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nano-cantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the distributed parameter model are compared with the lumped parameter model.     

Influence of size effect and elastic boundary condition on the pull-in instability of nano-scale cantilever beams immersed in liquid electrolytes

In this study, the static pull-in instability of nanocantilever beams immersed in a liquid electrolyte is theoretically investigated. In modeling the nanocantilever beam, the effects of van der Waals forces, elastic boundary condition and size dependency are considered. The modified couple stress theory, containing material length scale parameter, is used to interpret the size effect which appears in micro/nanoscale structures. The modified Adomian decomposition (MAD) method is used to gain an approximate analytical expression for the critical pull-in parameters which are essential for the design of micro/nanoactuators. The results show that the beam can deflect upward or downward, based on the values of the non-dimensional parameters. It is found that the size effect greatly influences the beam deflection and is more noticeable for small thicknesses. Neglecting size effect overestimates the deflection of the nanobeam. The findings reveal that the increase of ion concentration increases the pull-in voltage but decreases the pull-in deflection. Furthermore, an increase in ion concentration increases the influence of size-dependent effect on pull-in voltage.     

Dynamic pull-in phenomenon in MEMS resonators

We study the pull-in instability in microelectromechanical (MEMS) resonators and find that characteristics of the pull-in phenomenon in the presence of AC loads differ from those under purely DC loads. We analyze this phenomenon, dubbed dynamic pull-in, and formulate safety criteria for the design of MEMS resonant sensors and filters excited near one of their natural frequencies. We also utilize this phenomenon to design a low-voltage MEMS RF switch actuated with a combined DC and AC loading. The new switch uses a voltage much lower than the traditionally used DC voltage. Either the frequency or the amplitude of the AC loading can be adjusted to reduce the driving voltage and switching time. The new actuation method has the potential of solving the problem of high driving voltages of RF MEMS switches.     

Calibration of an optical tweezer microrheometer by sequential impulse response

We report a robust method for calibrating optical tweezers in any viscoelastic medium. This approach uses two coupled measurements—one from a static experiment in which a trapped particle diffuses passively within the tweezer’s harmonic potential and another from a dynamic experiment in which the trap is jumped discontinuously to a new position while the particle undergoes transient relaxation back into the minimum of the optical potential. Together, these are sufficient to determine the stiffness of the trap in a material of unknown rheology. The method is tested in a Newtonian fluid and compares favorably with other means of calibration. The calibration is also performed in a non-Newtonian fluid of which standard optical tweezer calibration methods may struggle to characterize. The correctly calibrated optical tweezer microrheometer measures the rheology of polymer solutions in agreement with macrorheological measurements.     

Electrostatic instability of the surface of a volume charged jet of dielectric liquid moving relative to the surrounding medium

The laws of implementation of electrostatic instability of the surface of a cylindrical volume charged jet of an ideal incompressible dielectric liquid moving relative to the ideal incompressible dielectric medium and the stability of bending-deformation capillary waves developed on the surface are investigated analytically. It is found that there are thresholds for the critical conditions of implementation of the instability with respect to the jet velocity relative to the medium (Weber number) and with respect to the electric space charge (relative to the ratio of the electrostatic pressure on the jet surface to the Laplace pressure). The critical analytic dependence between these dimensionless parameters is found.     

Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory

An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency(RF) micro electro-mechanical system(MEMS) switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.     

静电伺服微加速度计的量程设计

详细推导了静电伺服加速度计在定极板上施加直流偏压、交流驱动电压，动极板上有反馈直流电压和交流检测电压的情况下，检测质量(动极板)受到的静电力。通过对静电力的分析，得出静电伺服彻。速度计的量程除了受系统能提供的最大静电力限制外，还需满足电刚度小于与机械刚度的条件，该电刚度是极板上所有的直流电压、交流电压产生的电刚度之和。离心实验证明，利用该原则设计的“叉指”结构静电伺服微加速度计的量程达到了设计值。该设计原则可以为此类加速度计的设计提供参考。     

Analysis of dynamic pull-in voltage and response time for a micro-electro-mechanical oscillator made of power-law materials

Nonlinear Dynamics - Analysis of dynamic pull-in voltage for a micro-electro-mechanical oscillator of platform type is performed. The lumped mass model for the actuated micro-cantilever beam made...     

Upper and lower bounds for the pull-in parameters of a micro- or nanocantilever on a flexible support

An analytical method is proposed to accurately estimate the pull-in parameters of a micro- or nanocantilever beam elastically constrained by a rotational spring at one end. The system is actuated by electrostatic force and subject to Casimir or van der Waals forces according to the beam size. The deflection of the beam is described by a fourth-order nonlinear boundary value problem, or equivalently in terms of a nonlinear integral equation. New a priori analytical estimates on the solution from both sides are first derived and then lower and upper bounds for the pull-in parameters are obtained, with no need of solving the nonlinear boundary value problem. The lower and upper bounds turn out to be very close each other and in excellent agreement with the numerical results provided by the shooting method. The approach also provides accurate predictions for the pull-in parameters of a freestanding nanoactuator.     

静电陀螺监测器中静电陀螺仪的漂移误差模型

本推导了静电陀螺仪转子动量矩的运动方程,根据此方程并应用向量场理论,将造成静电陀螺漂移的外部干扰力矩划分为守恒力矩和非守恒力矩两部分。按照进动规律,最终得到静电陀螺监控器中陀螺仪漂移误差模型的全量形式。     

MEMS动平板的切向静电阻力

由于微机械的表面积与体积之比远大于宏机械,所以微机械中的表面阻力难以忽略,为了改善MEMS器件的性能和可靠性,必须对其影响进行研究.基于能量守衡法,本文建立了光滑平板和正方形、四棱锥两种微凸体粗糙表面平板的切向静电阻力模型,讨论了微小尺度、表面形貌、外加电压以及因流片制造工艺而产生的微凸体、凹坑或孔对两个相对运动的带电平板间的切向静电阻力的影响.分析表明：当平板宽度与两平板之间的距离之比、表面形貌因数和外加电压增大时,切向静电阻力也将随之增加;表面形貌因数则与微凸体在平板的总投影面积与平板面积之比成正比,随相对表面粗糙度增加而非线性增加.     

静电支承球形转子的恒速控制

本讨论静电支承球形转子的恒速控制问题。首先,介绍静电支承系统的基本工作原理,其次,建立静电支承系统的动力学模型。第三,分析采用PID控制器的支承刚度,第四,阐述形成静电旋转力矩的原理。最后,提出利用静电力恒速的方案与基本限制条件。     

Suppression of pull-in in a microstructure actuated by mechanical shocks and electrostatic forces

This work investigates the effect of a high-frequency voltage (HFV) on the pull-in instability in a microstructure actuated by mechanical shocks and electrostatic forces. The microstructure is modelled as a single-degree-of-freedom mass-spring-damper system. The method of direct partition of motion is used to split the fast and slow dynamics. Analysis of steady-state solutions of the slow dynamic allows the investigation of the influence of the HFV on the pull-in. The results show that adding HFV rigidifies the system, creates new stable equilibria and suppresses the pull-in instability for adequate high-frequency voltages. To illustrate the applicability of the result, a specific capacitive microelectromechanical system consisting of a clamped-clamped microbeam is considered.     

大冲击后力反馈微加速度计吸合失效与防止

冲击载荷强迫微加速度计的敏感质量大大偏离平衡位置,使差动静电力发生器的非线性效应体现出来,其结果是使正常工作时敏感质量仅在平衡位置附近有微小位移的状况下成立的负反馈闭环系统模型不再适用,敏感质量的受控特性可能变为正反馈,从而使微加速度计失效。为提高微加速度计受外界大载荷冲击后的可靠性,分析了加速度计的敏感质量在不同限制的静电反馈力下的受控特性及对应的闭环系统特性,推导了在已知止挡机械参数下确定微加速度计相应电气参数从而避免此类失效的防吸合准则。多次的验证实验表明,按防吸合准则设计了系统参数的静电力反馈加速度计,在受到远超过其本身量程的载荷冲击后,可以100%地防止吸合现象的出现。