Multi-objective design optimization of electrostatically actuated microbeam resonators with and without parameter uncertainty

Electrostatically actuated microbeam resonators are widely used components in microelectromechanical systems for sensing and signal filtering purposes. Due to the uncertainties resulting from manufacturing processes, material properties, and modeling assumptions, microbeam resonators may exhibit significant variations in their performance compared to nominal designs. There has been limited research on the performance prediction and the design optimization of such microsystems while accounting for relevant uncertainties. In this study, such uncertainties are considered in terms of the variability of parameters that define the dimensions, the material properties, and the operating conditions of the device. In addition, uncertainties with respect to a two-dimensional model of a microbeam resonator subject to electrostatic actuation are considered. A finite element model consisting of both the microbeam and the substrate is developed. The actuation forces are predicted by a reduced order electrostatic model, which accounts for the electromechanical interaction. A computationally efficient procedure is presented for simulating the steady-state dynamic response under electrostatic forces. The probabilistic performance of the microresonator is investigated using Monte Carlo simulation. A genetic algorithm is used to optimize the stochastic behavior of the microbeam resonator. The design is posed as combinatorial multi-objective optimization problem. Two design criteria describing the filter performance in terms of the shape of the frequency–response curve are simultaneously considered. The numerical results demonstrate the effectiveness of this procedure for the multi-objective optimization design of microbeam resonators and the importance of considering parameter uncertainty in the design of these devices.