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Shape optimizations and static/dynamic characterizations of deformable microplate structures with multiple electrostatic actuators

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Abstract

Micromirrors used in many optoelectronic devices can be considered as microplates. The functions and accuracy of the micromirrors depend on the static and dynamic deflection shapes of microplates. The objective of this study is to develop an efficient method for predicting the shapes of the microplates subjected to unsymmetrical electrostatic forces produced by electrostatic actuators such that micromirrors can be effectively optimized and controlled in their real time operation. The non-classical boundary conditions which result from the microfabrication process were modeled with artificial springs at the edges. A classical energy method using boundary characteristic orthogonal polynomials was applied to formulate the equations of motion of the microsystem. Based on this method, influence functions were built and least squares method was used to optimize the desired deflection under electrostatic forces from the electrostatic actuators. Softening effect of the electrostatic stiffness was also evaluated and considered in the simulation. Static deflections and dynamic responses were compared with those from finite element analysis (FEA) using Reduced Order Modeling (ROM) method. This study found that the static and dynamic responses of microplates predicted from the proposed method were highly consistent with those calculated from FEA. However, the proposed method is simpler and more efficient than FEA and can be conveniently used for any non-classical boundary condition situations. These features make the proposed method useful to effectively control and optimize the shape of a microplate with multiple electrostatic actuators.

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Authors and Affiliations

  1. Optical Microsystems Laboratory, Department of Mechanical and Industrial Engineering, Concordia University, 1455, De Maisonneuve Blvd. West, Montreal, QC, Canada, H3G 1M8

    Yunqiang Li, Muthukumaran Packirisamy & Rama B. Bhat

  2. Department of Mechanical and Industrial Engineering, Concordia University, Sir George Williams Campus, 1515 St. Catherine W., EV013.235, Montreal, QC, Canada, H3G 2W1

    Yunqiang Li

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  1. Yunqiang Li
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  2. Muthukumaran Packirisamy
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  3. Rama B. Bhat
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Correspondence to Yunqiang Li.

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Li, Y., Packirisamy, M. & Bhat, R.B. Shape optimizations and static/dynamic characterizations of deformable microplate structures with multiple electrostatic actuators. Microsyst Technol 14, 255–266 (2008). https://doi.org/10.1007/s00542-007-0420-3

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  • DOI: https://doi.org/10.1007/s00542-007-0420-3

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