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An eigenvalue analysis of a tunable micro-mechanical actuator is presented. The actuator is modeled as a continuum structure. The eigenvalue modified by the tuning voltage is computed through the linearization of the relation between the electrostatic force and the displacement at the equilibrium. A staggered algorithm is employed to perform the coupled analysis of the electrostatic and elastic fields. The stiffness matrix of the acti.iator is modified at this equilibrium state. The displacement field is perturbed using an eigenmode profile of the actuator. The configuration change of the actuator due to perturbation modifies the electrostatic field and thus the electrostatic force. The equivalent stiffness matrix corresponding to the perturbation and the change in the electrostatic force is then added to stiffness matrix in order to explain natural frequency shifting. The numerical examples are presented and compared with the experiments in the literatures.

The continuous thin-plate type with discrete actuators is widely used for active or adaptive mirrors in the medium size range from about 10cm up to 2m in diameters. The performance of a thin-plate deformable mirror could be characterized by the influence function of an actuator and the layout of the actuators. This paper first derives an equation which estimates influence functions of thin-plate deformable mirrors based on the analytic calculation and finite element analysis. Then the performance analysis for the case of equi-spaced actuators is presented.

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A parallel method to solve large eigenvalue problems using dynamic substructuring and homotopy continuation is presented. Unlike the conventional approaches in substructuring, the non-linear term is not neglected for improved accuracy. Therefore, instead of solving the approximated condensed problems, full exact condensed forms are treated. Homotopy continuation method is introduced to solve the non-linear reduced eigenvalue problem. In the process small number of substructure modes are used to reduce the original eigenvalue problem, and additional degrees of freedom, besides those at interfaces, are selected. The whole procedures are implemented to workstation cluster using PVM.To show how the method works, simple two-dimensional numerical examples are solved. It is demonstrated that the method yields highly accurate results and good parallel efficiency.1998 John Wiley & Sons, Ltd.