A wide range of microelectromechanical systems (MEMSs) and devices are actuated using electrostatic forces. Multiphysics modeling is required, since coupling among different fields such as solid and fluid mechanics, thermomechanics and electromagnetism is involved. This work presents an overview of models for electrostatically actuated MEMSs. Three-dimensional nonlinear formulations for the coupled electromechanical fluid-structure interaction problem are outlined. Simplified reduced-order models are illustrated along with assumptions that define their range of applicability. Theoretical, numerical and experimental works are classified according to the mechanical model used in the analysis.
We consider the von Kármán nonlinearity and the Casimir force to develop reduced-order models for prestressed clamped rectangular and circular electrostatically actuated microplates. Reduced-order models are derived by taking flexural vibration mode shapes as basis functions for the transverse displacement. The in-plane displacement vector is decomposed as the sum of displacements for irrotational and isochoric waves in a two-dimensional medium. Each of these two displacement vector fields satisfies an eigenvalue problem analogous to that of transverse vibrations of a linear elastic membrane. Basis functions for the transverse and the in-plane displacements are related by using the nonlinear equation governing the plate in-plane motion. The reduced-order model is derived from the equation yielding the transverse deflection of a point. For static deformations of a plate, the pull-in parameters are found by using the displacement iteration pull-in extraction method. Reduced-order models are also used to study linear vibrations about a predeformed configuration. It is found that 9 basis functions for a rectangular plate give a converged solution, while 3 basis functions give pull-in parameters with an error of at most 4%. For a circular plate, 3 basis functions give a converged solution while the pull-in parameters computed with 2 basis functions have an error of at most 3%. The value of the Casimir force at the onset of pull-in instability is used to compute device size that can be safely fabricated.
Abstract:The nonverbal transmission of information between social animals is a primary driving force behind their actions and, therefore, an important quantity to measure in animal behavior studies. Despite its key role in social behavior, the flow of information has only been inferred by correlating the actions of individuals with a simplifying assumption of linearity. In this paper, we leverage information-theoretic tools to relax this assumption. To demonstrate the feasibility of our approach, we focus on a robotics-based experimental paradigm, which affords consistent and controllable delivery of visual stimuli to zebrafish. Specifically, we use a robotic arm to maneuver a life-sized replica of a zebrafish in a predetermined trajectory as it interacts with a focal subject in a test tank. We track the fish and the replica through time and use the resulting trajectory data to measure the transfer entropy between the replica and the focal subject, which, in turn, is used to quantify one-directional information flow from the robot to the fish. In agreement with our expectations, we find that the information flow from the replica to the zebrafish is significantly more than the other way around. Notably, such information is specifically related to the response of the fish to the replica, whereby we observe that the information flow is reduced significantly if the motion of the replica is randomly delayed in a surrogate dataset. In addition, comparison with a control experiment, where the replica is replaced by a conspecific, shows that the information flow toward the focal fish is significantly more for a robotic than a live stimulus. These findings support the reliability of using transfer entropy as a measure of information flow, while providing indirect evidence for the efficacy of a robotics-based platform in animal behavioral studies.
Abstract-We consider the problem of estimating the state of a system when measurement noise is a function of the system's state. We propose generalizations of the extended Kalman filter and the iterated extended Kalman filter that can be utilized when the state estimate distribution is approximately Gaussian. The state estimate is computed by an iterative root-searching method that maximizes a maximum likelihood function. The new filter allows for the consistent treatment of a class of control problem involving nonlinear estimation from measurements with statedependent noise. The effectiveness of the estimation algorithm is illustrated for a control problem with a mobile bearing-only sensor.
PACS 03.65.Sq-Semiclassical theories and applications PACS 07.10.Cm-Micromechanical devices and systems PACS 85.85.+j-Micro-and nano-electromechanical systems (MEMS/NEMS) and devices Abstract-We analyze pull-in instability of electrostatically actuated microelectromechanical systems, and study changes in pull-in parameters due to the Casimir effect. When the size of the device is reduced, the magnitude of the Casimir force is comparable with that of the Coulomb force and it significantly alters pull-in parameters. We model the deformable conductor as an elastic membrane and consider different geometries. Beyond a certain critical size the pull-in instability occurs with zero applied voltage, and the device may collapse during the fabrication process.
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