This paper deals with the nonlinear response of electrostatically actuated cantilever beam microresonators near-half natural frequency. A¯rst-order fringe correction of the electrostatic force, viscous damping, and Casimir e®ect are included in the model. Both forces, electrostatic and Casimir, are nonlinear. The dynamics of the resonator is investigated using the method of multiple scales (MMS) in a direct approach of the problem. The reduced order model (ROM) method, based on Galerkin procedure, is used as well. Steady-state motions are found. Numerical simulations are conducted for uniform microresonators. The in°uences of damping, actuation, and fringe e®ect on the resonator response are found. NomenclatureConstants " 0 ¼ 8:854 Â 10 À12 C 2 N À1 m À2 Permittivity of free space } ¼ 1:055 Â 10 À34 J Á s Dirac constant c ¼ 2:998 Â 10 8 m Á s À1 Speed of light ¼ 1:85 Â 10 À5 kg Á m À1 s À1

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

No abstract

We present a novel adaptive color mapping method for virtual objects in mixed-reality environments. In several mixed-reality applications, added virtual objects should be visually indistinguishable from real objects. Recent mixed-reality methods use globalillumination algorithms to approach this goal. However, simulating the light distribution is not enough for visually plausible images. Since the observing camera has its very own transfer function from real-world radiance values to RGB colors, virtual objects look artificial just because their rendered colors do not match with those of the camera.Our approach combines an on-line camera characterization method with a heuristic to map colors of virtual objects to colors as they would be seen by the observing camera. Previous tonemapping functions were not designed for use in mixed-reality systems and thus did not take the camera-specific behavior into account. In contrast, our method takes the camera into account and thus can also handle changes of its parameters during runtime. The results show that virtual objects look visually more plausible than by just applying tone-mapping operators.

No abstract