Analysis of the response of a simply supported microbeam subject to an electric actuation
J.G. Rou (TU Delft - Electrical Engineering, Mathematics and Computer Science)
WT van Horssen – Mentor (TU Delft - Mathematical Physics)
IM Blanter – Mentor (TU Delft - QN/Blanter Group)
H.S.J. van der Zant – Graduation committee member (TU Delft - QN/van der Zant Lab)
C. Vuik – Graduation committee member (TU Delft - Numerical Analysis)
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Abstract
In this research a study of the response of a simply supported microbeam subject to an electric actuation is presented. A perturbation method called the method of multiple scales is explained and used to solve our problem. A model concerning the mid-plane stretching and an electric force with a direct and alternating current component is formulated. The method of multiple scales is used to construct a solution that is valid for a long time after the initial conditions. The effect of the frequency of the alternating current was studied by performing a stability analysis. The results show that for frequencies close to the eigenfrequency of the homogeneous problem, there is no stable equilibrium and resonance occurs. Furthermore, a start was made to study the effect of the damping coefficient. The results show that a smaller damping will always lead to resonance on a very small time scale. The results also indicate larger oscillations and an small increase of the importance of the non-linear terms for smaller damping. All results are validated by comparing them with a numeric solution and show excellent agreement.