Application of Iteration Perturbation Method in studying dynamic pull-in instability of micro-beams

Abstract

In the present study, dynamic pull-in instability of electrostatically-actuated micro-beams is investigated through proposing the nonlinear frequency amplitude relationship. An approximate analytical expression of the fundamental natural frequency is presented by modern asymptotic approach namely Iteration Perturbation Method (IPM). Influences of vibrational amplitude as well as different parameters on dynamic pull-in voltage are investigated. It is demonstrated that two terms in series expansions is sufficient to produce an acceptable solution of the mentioned microstructure. The simulations from numerical methods verify the validity of the analytical procedure.

Online Test Structure for Measuring Young’s Modulus and Residual Stress of the Top Silicon Layer of Silicon-On-Insulator by a Pull-in Approach

“…(7) At a critical pull-in voltage, the beam becomes unstable and spontaneously collapses to the electrode. (5) When the beam deflects, an excess stress Δσ is produced along the beam and remains constant in accordance with the theory of elasticity. The deflection curve can be expressed as (11,12) …”

“…(2) To provide information regarding material parameters for MEMS engineers both for design and optimization, it is nesseary to extract material properties for a given process. (3)(4)(5) The theory of electrostatic pull-in bias has been well documented by Petersen. (6) Afterwards, Najafi and Suzuki, (7) and Osterberg and Senturia have rectified the structure.…”

“…(8) It will result in a certain deviation because we make numerous hypotheses and simplify the structure, besides the effects of gravity and the release process. (5,9) Silicon-on-insulator (SOI) wafers are precisely engineered multilayer semiconductor structures that provide new functionalities to advanced Si devices. SOI technology offers significant advantages in the design, fabrication, and performance of many semiconductor circuits.…”

Static and Dynamic Pull-In Instability of Nano-Beams Resting on Elastic Foundation Based on the Nonlocal Elasticity Theory

“…By employing Homotopy Perturbation Method with an auxiliary term, he obtained the high-order frequency-amplitude relation and investigated the influences of material properties and actuation voltage on dynamic pull-in behavior of microstructures. Sedighi et al [19] studied dynamic pull-in instability of electrostatically-actuated micro-beams by proposing the nonlinear frequency amplitude relationship using Iteration Perturbation Method (IPM). They demonstrated that two terms in series expansions is sufficient to produce an acceptable solution of the micro-structure.…”

DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory

“…Among the nanostructures, carbon nanotubes (CNTs) are one of the most important structures which are regarded as representatives for nanotechnology due to their unique characteristics. These structures have outstanding mechanical, physical and chemical properties such as high strength, high stiffness to weight ratio, as well as high electrical and thermal conductivity (Ruoff and Lorents, 1995;Tans et al, 1998;Tombler et al, 2000;Jiang et al, 2004;Friedman et al, 2005;Sedighi et al, 2014).…”