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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 review crane models available in the literature, classify them, and discuss their applications and limitations. A generalized formulation of the most widely used crane model is analyzed using the method of multiple scales. We also review crane control strategies in the literature, classify them, and discuss their applications and limitations. In conclusion, we recommend appropriate models and control criteria for various crane applications and suggest directions for further work.

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 architecture for wideband vibration-based micro-power generators (MPGs). It replaces a linear oscillator with a piecewise-linear oscillator as the energy harvesting element of the MPG. A prototype of an electromagnetic MPG designed accordingly is analyzed analytically, numerically and experimentally. We find that the new architecture increases the bandwidth of the MPG during a frequency up-sweep, while maintaining the same bandwidth in a down-sweep. Closed-form expressions for the response of the new MPG as well as the up-sweep bandwidth are presented and validated experimentally. Simulations show that under random-frequency excitations, the new MPG collects more energy than the traditional MPG.

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.

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We investigate the response of a microbeam-based resonant sensor to superharmonic and subharmonic electric actuations using a model that incorporates the nonlinearities associated with moderately large displacements and electric forces. The method of multiple scales is used, in each case, to obtain two first-order nonlinear ordinary-differential equations that describe the modulation of the amplitude and phase of the response and its stability. We present typical frequency-response and force-response curves demonstrating, in both cases, the coexistence of multivalued solutions. The solution corresponding to a superharmonic excitation consists of three branches, which meet at two saddle-node bifurcation points. The solution corresponding to a subharmonic excitation consists of two branches meeting a branch of trivial solutions at two pitchfork bifurcation points. One of these bifurcation points is supercritical and the other is subcritical. The results provide an analytical tool to predict the microsensor response to superharmonic and subharmonic excitations, specifically the locations of sudden jumps and regions of hysteretic behavior, thereby enabling designers to safely use these frequencies as measurement signals. They also allow designers to examine the impact of various design parameters on the device behavior.