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This work studies the dynamic behavior of electrostatic actuators using finite-element package software (FEMLAB) and differential quadrature method. The differential quadrature technique is used to transform partial differential equations into a discrete eigenvalue problem. Numerical results indicate that length, width, and thickness significantly impact the frequencies of the electrostatic actuators. The thickness could not affect markedly the electrostatic actuator capacities. The effects of varying actuator length, width, and thickness on the dynamic behavior and actuator capacities in electrostatic actuator systems are investigated. The differential quadrature method is an efficient differential equation solver.

Plate-type electrostatic actuators are widely applied in microelectromechanical systems. Microelectrostatic actuator devices have a high operating frequency, low-power consumption and can replace many passive components. Mehdaoui et al. [

Figure

Schematic view of electrostatic actuator.

Capacities of microelectrostatic actuator for various lengths.

Capacities of microelectrostatic actuator for various widths.

Capacities of microelectrostatic actuator for various gap distances.

Capacities of microelectrostatic actuator for various thicknesses.

The electrostatic actuator has length

The commercially available FEMLAB software package is used to evaluate dynamic problems based on partial differential equations. To derive finite formulations, the following virtual work principle must be utilized in the following equations [

The vibration response of the microactuator is numerically modeled using the differential quadrature method in this work. The differential quadrature method is used to convert the partial differential equations of the plates into a discrete eigenvalue problem. The roots of shifted Chebyshev and Legendre sampling point equation are used to select the sampling points in these analyses. The integrity and computational efficiency of the differential quadrature method in this problem is demonstrated below in several case studies. The differential quadrature method is a relatively new method that was introduced by Bellman and Casti [

The material parameters of the electrostatic actuator are ^{3} and

The lowest six frequencies of electrostatic actuator for various lengths.

The lowest six frequencies of electrostatic actuator for various widths.

The lowest six frequencies of electrostatic actuator for various thicknesses.

Numerical results indicate that length and width significantly impact the capacity of electrostatic microactuator. The presented formulation reveals that the differential quadrature approach is convenient for solving problems governed by fourth- or higher-order differential equations. Simulation results verify that the differential quadrature method obtains accurate results with relatively minimal computational and modeling efforts. Length, width, and thickness can markedly affect electrostatic microactuator frequencies. The FEMLAB can handle capacitance and dynamic problems as well. The differential quadrature methodology may be further examined to solve more complicated problems or in other fields of science.