Analysis of the mechanical behavior of a doubled microbeam configuration under electrostatic actuation

• The mechanical behavior of a doubled microbeam configuration is analyzed under electrostatic actuation.
• Increasing the free–free microbeam length increases the static deflection and decreases both of the pull-in voltage and natural frequency.
• There is a special dimension for system that the mechanical behavior is the same for both of single and doubled microbeam configurations.

In this paper, the deflection and natural frequency of a doubled microbeam configuration under electrostatic actuation are studied. This configuration consists of a clamped–clamped microbeam while a free–free microbeam is attached to it. The DC electrostatic voltage is applied between the free–free microbeam and the opposite electrode plate. The importance of this model is in its uniform displacement which is useful for microsensor applications. The static deflection, pull-in voltage and natural frequency are studied using three methods of modeling. In the first model, the set of free–free microbeam and the attached segment of clamped–clamped microbeam to it are modeled as a rigid body between two flexible Euler–Bernouli microbeams. The equations of motion and associated continuity conditions are derived using Newton second law. A closed form solution is found for static deflection and vibration about this position. In the second model, the dynamic effect of free–free microbeam is modeled as a concentrated force and moment, and it is introduced by the aid of Dirac function in the motion equation. The equations of motion are solved using Galerkin method. The mode shapes of the clamped–clamped microbeam are employed as comparison functions. The third model is a finite element model using the commercial software, ANSYS. The verification of the solutions is carried out by comparing the results of three considered models and also comparing with previous works. The mechanical behavior of the considered configuration is compared with the mechanical behavior of the single microbeam configuration. The results demonstrate that there is a special geometry for free–free microbeam where the mechanical behavior in both single and doubled microbeam configuration would be approximately the same. This is a useful result, because the doubled microbeam configuration has a uniform displacement which is a main advantage in the design of microsensors.