Effects of voltage change on the dynamics in a comb-drive finger of an electrostatic actuator

Periodic solutions of the Nathanson’s and the Comb-drive models

“…prove the existence of symmetric periodic solutions for other electrostatic actuator known in the literature as a Comb-drive finger. Motivated by the successful use of well-developed mathematical techniques for the study of some canonical MEMS, the aim of this document is provide sufficient conditions for the existence and stability of periodic solutions of the equation of motions of two special types of electrostatic actuators, namely, the Nathanson's model (or Parallel-Plate capacitor model) which is based on the resonant gate transistor [14] and the Comb-drive finger model [8,21].…”

“…Up to our knowledge, the first mathematical analysis of periodic solutions for the Nathanson's model appears in [2] (2007) by means of shooting techniques and later in [9] (2013) using degree theory and lower and upper solution method where the authors prove the existence, multiplicity and stability of periodic solutions. Recently in [8] (2017) using the Leray-Schauder continuation theorem, the authors…”

Nonlinear oscillation of a microbeam due to an electric actuation—Comparison of approximate models

“…Meanwhile, in the theory under consideration, essential nonlinear effects are of interest, which cannot be described in the quasilinear approximation. In particular, it is important to avoid the collision between the movable finger and the fixed groundplate [15][16][17]. This undesirable effect known as pull-in or pull-in instability could lead to damage of the device.…”

“…The pull‐in phenomenon studied by many authors both analytically and numerically. In particular, phenomenological one dof models such as Nathanson (or parallel‐plate capacitor model) [5] or comb‐drive ones [17] have been used.…”