Modeling and simulations of collapse instabilities of microbeams due to capillary forces

Hassen M. Ouakad, Mohammad I. Younis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

We present modeling and analysis for the static behavior and collapse instabilities of doubly-clamped and cantilever microbeams subjected to capillary forces. These forces can be as a result of a volume of liquid trapped underneath the microbeam during the rinsing and drying process in fabrication. The model considers the microbeam as a continuous medium, the capillary force as a nonlinear function of displacement, and accounts for the mid-plane stretching nonlinearity. The capillary force is assumed to be distributed over a specific length underneath the microbeam. The Galerkin procedure is used to derive a reduced-order model consisting of a set of nonlinear algebraic and differential equations that describe the microbeams static and dynamic behaviors. We study the collapse instability, which brings the microbeam from its unstuck configuration to touch the substrate and gets stuck in the so-called pinned configuration. We calculate the pull-in length that distinguishes the free from the pinned configurations as a function of the beam thickness and gap width for both microbeams. Comparisons are made with analytical results reported in the literature based on the Ritz method for linear and nonlinear beam models. The instability problem, which brings the microbeam from a pinned to adhered configuration is also investigated. For this case, we use a shooting technique to solve the boundary-value problem governing the deflection of the microbeams. The critical microbeam length for this second instability is also calculated.

Original languageEnglish
Title of host publication2008 Proceedings of ASME International Mechanical Engineering Congress and Exposition, IMECE 2008
Pages187-195
Number of pages9
EditionPART A
DOIs
Publication statusPublished - Sep 21 2009
Externally publishedYes
Event2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008 - Boston, MA, United States
Duration: Oct 31 2008Nov 6 2008

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings
NumberPART A
Volume13

Conference

Conference2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008
CountryUnited States
CityBoston, MA
Period10/31/0811/6/08

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Ouakad, H. M., & Younis, M. I. (2009). Modeling and simulations of collapse instabilities of microbeams due to capillary forces. In 2008 Proceedings of ASME International Mechanical Engineering Congress and Exposition, IMECE 2008 (PART A ed., pp. 187-195). (ASME International Mechanical Engineering Congress and Exposition, Proceedings; Vol. 13, No. PART A). https://doi.org/10.1115/IMECE2008-67502