In this paper the electromechanical behavior of a torsional micromirror was investigated using of a static model with considering torsion and bending characteristics of micro-beams. A set of nonlinear equations based on the parallel plate capacitor model was derived to represent the relationships between the applied voltage, torsion angle, and vertical displacement of the torsional micromirror.Step by step linearization method (Newton's method) was used to calculate the rotation angle and vertical displacement of the micromirror due to the applied voltage. This method is fast and gave acceptable and accurate results which were in good agreement with the experimental data.
In this paper dynamic characteristics of a capacitive torsional micromirror under electrostatic forces and mechanical shocks have been investigated. A 2DOF model considering the torsion and bending stiffness of the micromirror structure has been presented. A set of nonlinear equations have been derived and solved by RungeKutta method. The Static pull-in voltage has been calculated by frequency analyzing method, and the dynamic pull-in voltage of the micromirror imposed to a step DC voltage has been derived for different damping ratios. It has been shown that by increasing the damping ratio the dynamic pull-in voltage converges to static one. The effects of linear and torsional shock forces on the mechanical behavior of the electrostatically deflected and undeflected micromirror have been studied. The results have shown that the combined effect of a shock load and an electrostatic actuation makes the instability threshold much lower than the threshold predicted, considering the effect of shock force or electrostatic actuation alone. It has been shown that the torsional shock force has negligible influence on dynamic response of the micromirror in comparison with the linear one. The results have been calculated for linear shocks with different durations, amplitudes, and input times.
In this paper a numerical simulation of unsteady sheet cavitation is presented as it occurs on an NACA-0015 hydrofoil. The computational approach is based on the Euler equations for unsteady compressible flow, using an equilibrium cavitation model of Schnerr, Schmidt, and Saurel. It was found that for a computational method that directly uses the thermodynamic closure relations, more than 90% of the computational time was spent in computations associated with these relations. To circumvent this problem, the computationally costly method is replaced by using precomputed multiphase thermodynamic tables containing the same information, with no need to determine the flow phase. The thermodynamic computations using this approach are almost instantaneous. However, preparing these multiphase tables is not straightforward. The main difficulty is due to the slope discontinuities in the phase-transitioning regions of the multiphase tables. In these regions, the conventional look-up approaches are inaccurate and inefficient (their accuracy is insensitive to data grid refinement). To remove this bottleneck, phase-oriented interpolations in transition cells is developed as a novel approach that allows for preparing much more accurate and efficient (much smaller size) multiphase thermodynamic tables compared to conventional interpolation approaches.
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