), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my parents Ibrahim and Halemah My wife Ola and our sons Ibrahim, Muhmoud, and Mutaz PrefaceSeveral decades have passed by since the discovery and development of microelectro-mechanical systems (MEMS). This technology has reached a level of maturity that, today, several MEMS devices are being used in our every-day life, ranging from accelerometers and pressure sensors in cars, micro-mirrors in Plasma TVs, radiofrequency (RF) switches and microphones in cell phones, and inertia sensors in video games. Fabrication methods of MEMS, such as bulk and surface micromachining, are now well-known and almost standardized. Nowadays, hundreds of foundries around the world offer numerous fabrication services that can translate the imagination of a MEMS designer of a device into reality.Even with the maturity of fabrication and commercialization, MEMS is still one of the hottest evolving areas in science and engineering, where scientists from across various disciplines investigate, brainstorm, and collaborate to invent smarter devices, develop new technologies, and innovate unique solutions. With the increasing pressure for sensors and actuators of sophisticated functionalities, which are self-powered, self-calibrated, and self-tested, MEMS are expected to remain the sought-after technology of scientists for many years to come. However, with this growing demand on the MEMS technology come great challenges. Designers are now aiming to achieve complicated objectives while meeting a long list of specifications related to sensitivity, fabrication, system integration, packaging, and reliability. These challenges have created a motivation to seek new solutions and ideas, beyond changing the geometry of devices and making more complex configurations. Researchers are starting to realize the need to look into new methods of improvement and innovation in MEMS beyond the static laws of design and the limitations of linear theories. It is realized now that linear theories are too shallow to allow for bolder ideas and more aggressive design goals. More attention is being directed to investigate deeply the dynamics and motion aspects of MEMS and to explore the hidden opportunities of operating MEMS in the nonlinear regimes.Most MEMS devices employ a structure or more that undergoes some sort of motion. Accelerometers, gyroscopes, micromirrors, microphones, resonators and oscillators, RF switches and filters, and thermal actuators are f...

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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.

We present a nonlinear model of electrically actuated microbeams accounting for the electrostatic forcing of the air gap capacitor, the restoring force of the microbeam and the axial load applied to the microbeam. The boundary-value problem describing the static deflection of the microbeam under the electrostatic force due to a dc polarization voltage is solved numerically. The eigenvalue problem describing the vibration of the microbeam around its statically deflected position is solved numerically for the natural frequencies and mode shapes. Comparison of results generated by our model to the experimental results shows excellent agreement, thus verifying the model. Our results show that failure to account for mid-plane stretching in the microbeam restoring force leads to an underestimation of the stability limits. It also shows that the ratio of the width of the air gap to the microbeam thickness can be tuned to extend the domain of the linear relationship between the dc polarization voltage and the fundamental natural frequency. This fact and the ability of the nonlinear model to accurately predict the natural frequencies for any dc polarization voltage allow designers to use a wider range of dc polarization voltages in resonators.

We present a new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping. Our approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the electrostatic forcing of the capacitor airgap, the restoring force of the microplate and the applied in-plane loads. It also accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions, the natural frequencies and the quality factors. We apply the new approach to a variety of rectangular and circular plates and present the final expressions for the pressure distributions and quality factors. Our theoretically calculated quality factors are in excellent agreement with available experimental data and hence our methodology can be used to simulate accurately the dynamics of flexible microstructures and predict their quality factors under a wide range of gas pressures. Because the pressure distribution is related analytically to the deflection, the dimension of the coupled structural-fluidic problem and hence the number of global variables needed to describe the dynamics of the system is reduced considerably. Consequently, the new approach can be significant to the development of computationally efficient CAD tools for microelectromechanical systems.

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We present an analysis and simulations for the dynamics of electrically actuated microbeams under secondary resonance excitations. The presented model and methodology enable simulation of the transient and steady-state dynamics of microbeams undergoing small or large motions. The microbeams are excited by a dc electrostatic force and an ac harmonic force with a frequency tuned near twice their fundamental natural frequencies (subharmonic excitation of order one-half) or half their fundamental natural frequencies (superharmonic excitation of order two). In the case of superharmonic excitation, we present results showing the effect of varying the dc bias, the damping and the ac excitation amplitude on the frequency–response curves. In the case of subharmonic excitation, we show that, once the subharmonic resonance is activated, all frequency–response curves reach pull-in, regardless of the magnitude of the ac forcing. We conclude that the quality factor has a limited influence on the frequency response in this case. This result and the fact that the frequency–response curves have very steep passband-to-stopband transitions make the combination of a dc voltage and a subharmonic excitation of order one-half a promising candidate for designing improved high-sensitive RF MEMS filters. For both excitation methods, we show that the dynamic pull-in instability can occur at an electric load much lower than a purely dc voltage and of the same order of magnitude as that in the case of primary-resonance excitation.

We review the development of reduced-order models for MEMS devices. Based on their implementation procedures, we classify these reduced-order models into two broad categories: node and domain methods. Node methods use lower-order approximations of the system matrices found by evaluating the system equations at each node in the discretization mesh. Domainbased methods rely on modal analysis and the Galerkin method to rewrite the system equations in terms of domain-wide modes (eigenfunctions). We summarize the major contributions in the field and discuss the advantages and disadvantages of each implementation. We then present reduced-order models for microbeams and rectangular and circular microplates. Finally, we present reduced-order approaches to model squeeze-film and thermoelastic damping in MEMS and present analytical expressions for the damping coefficients. We validate these models by comparing their results with available theoretical and experimental results. State-of-the-ArtThe dynamics of MEMS are represented by partial-differential equations (PDEs) and associated boundary conditions. The most widely used method to treat these distributed-parameter problems is to reduce them to ordinary-differential equations (ODEs) in time and then solve the reduced equations either numerically or analytically. Three approaches are used in the reduction.• Idealization of the device flexible structural elements as rigid bodies.• Discretization using finite-element methods (FEM), boundary-element methods (BEM), or finitedifference methods (FDM). • Construction of reduced-order models (ROM).The first and second approaches, while lying at opposite extremes of complexity, are currently the most widely used. The pressure for better designs, less trial-and-error in the design process, and better device performance demands better models than idealized rigid bodies. Numerous researchers compared the pull-in voltage of electrostatically actuated cantilever [1] and clamped-clamped [2] microbeams obtained by solving the distributed-parameter system to those obtained using a spring-mass model and found that the spring-mass model underpredicts the pull-in voltage.Although FEM/BEM and FDM simulations are adequate for the analysis of the static deflections (equilibrium positions) of MEMS devices, they are inadequate for dynamic simulations because they require the time integration of thousands of second-order ODEs (one for each degree of freedom in the model). This is a very expensive process, making system-level simulation, device optimization, interactive design, and evolutionary design almost impossible. As a result, reduced-order modeling of MEMS is gaining attention as a way to balance the need for enough fidelity in the model against the numerical efficiency necessary to make the model of practical use in MEMS design.