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The undamped dynamic response of electrostatic MEMS switches that are driven by a step-function voltage is investigated. A systematic analysis using energy methods is presented. An analytic expression for switching time is derived and this expression may be used as a design rule for electrostatic switches. The analytic predictions are validated experimentally using test structures with parallel-plates actuators. It is shown that the analysis is also applicable for switches with more general geometry. [2007-0059] Index Terms--Dynamic pull-in, dynamic response, electrostatic actuators, electrostatic switches.

A first-ever experimental validation of the electromechanical buckling response is presented. Electromechanical buckling is the coupling of two bifurcation responses: mechanical buckling and electromechanical bifurcation. In this paper, electromechanical buckling is demonstrated on a clamped-guided beam that is simultaneously subjected to an axial mechanical load and a symmetric, transverse, electrostatic field. Experimental measurements of the electromechanical buckling voltage are in good agreement with the theoretical prediction. Index Terms--Electromechanical buckling, electromechanical instability.

A novel method and test structure for measuring the strength of brittle microbeams is presented. The method does not require any measurement of forces or displacements. The test structure includes a microbeam that is wrapped over a curved side-wall by application of an unmeasured force. With the progression of wrapping, increasing tensile stresses are induced in the microbeam. When sufficiently high stresses are induced, the beam breaks. The failure stress is deduced by measuring the length of the remaining ligament of the broken beam. The method is demonstrated by measuring the strength of microbeams in bulk-micromachined test structures. [1471] Index Terms--Mechanical test device, strength of microstructures.

This study considers the dynamic response of electrostatic actuators with multiple degrees of freedom that are driven by multiple voltage sources. The critical values of the applied voltages beyond which the dynamic response becomes unstable are investigated. A methodology for extracting a lower bound for this dynamic pull-in voltage is proposed. This lower bound is based on the stable and unstable static response of the system, and can be rapidly extracted because it does not require time integration of momentum equations. As example problems, the dynamic pull-in of two prevalent electrostatic actuators is analyzed. [1334] Index Terms--Dynamic pull-in, electrostatic actuation.

The constitutive equations of multilayered piezoelectric structures are derived in a new form. In this form, the electromechanical coupling is presented as an additional stiffness matrix. This matrix is a true property of the piezoelectric structure and is independent of specific mechanical boundary conditions that may apply to the structure. A novel model of the electromechanical response of such structures is presented. This model accounts for the three-dimensional (3-D) kinematics of the structure deformation. Solution of example problems using the new model shows excellent agreement with full 3-D finite element simulations. These solutions are also compared to the results of previous two-dimensional (2-D) model approximations presented in literature, and the inaccuracies associated with these previous models are discussed. [1114] Index Terms--Electromechanical coupling, multimorphs, piezoelectricity, smart structures.

This work presents a systematic analysis of electrostatic actuators driven by multiple uncoupled voltage sources. The use of multiple uncoupled voltage sources has the potential of enriching the electromechanical response of electrostatically actuated deformable elements. This in turn may enable novel MEMS devices with improved and even new capabilities. It is therefore important to develop methods for analyzing this class of actuators. Pull-in is an inherent instability phenomenon that emanates from the nonlinear nature of the electromechanical coupling in electrostatic actuators. The character of pull-in in actuators with multiple uncoupled voltage sources is studied, and new insights regarding pull-in are presented. An analytical method for extracting the pull-in hyper-surface by directly solving the voltage-free K-N pull-in equations derived here, is proposed. Solving simple but interesting example problems illustrate these new insights. In addition, by using current methods. [898] Index Terms--Electrostatic actuator, multiple voltage sources, pull-in.

Pull-in parameters are important properties of electrostatic actuators. Efficient and accurate analysis tools that can capture these parameters for different design geometries, are therefore essential. Current simulation tools approach the Pull-In state by iteratively adjusting the voltage applied across the actuator electrodes. The convergence rate of this scheme gradually deteriorates as the Pull-In state is approached. Moreover, the convergence is inconsistent and requires many mesh and accuracy refinements to assure reliable predictions. As a result, the design procedure of electrostatically actuated MEMS devices can be time-consuming. In this paper a novel displacement iteration Pull-In extraction (DIPIE) scheme is presented. The DIPIE scheme is shown to converge consistently and far more rapidly than the voltage iterations (VI) scheme (> 100 times faster!). The DIPIE scheme requires separate mechanical and electrostatic field solvers. Therefore, it can be easily implemented in existing MOEMS CAD packages. Moreover, using the DIPIE scheme, the Pull-In parameters extraction can be performed in a fully automated mode, and no user input for search bounds is required. [782] Index Terms--Actuator, computer-aided design (CAD), displacement iteration Pull-In extraction (DIPIE), electrostatic, Pull-In.