Abstract
We provide sufficient conditions for the existence of periodic solutions for an idealized electrostatic actuator modeled by the Liénard-type equation x ¨ + F D x , x ̇ + x = β V 2 t / 1 − x 2 , x ∈ − ∞ , 1 with β ∈ ℝ + , V ∈ C ℝ / T ℤ , and F D x , x ̇ = κ x ̇ / 1 − x 3 , κ ∈ ℝ + (called squeeze film damping force), or F D x , x ̇ = c x ̇ , c ∈ ℝ + (called linear damping force). If F D is of squeeze film type, we have proven that there exists at least two positive periodic solutions, one of them locally asymptotically stable. Meanwhile, if F D is a linear damping force, we have proven that there are only two positive periodic solutions. One is unstable, and the other is locally exponentially asymptotically stable with rate of decay of c / 2 . Our technique can be applied to a class of Liénard equations that model several microelectromechanical system devices, including the comb-drive finger model and torsional actuators.
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