Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary Forces

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....

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Main Authors: Hassen M. Ouakad, Mohammad I. Younis
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2009/871902
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spelling doaj-22d1b88066034826a8cc42f9aeffd0ef2020-11-25T00:56:35ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472009-01-01200910.1155/2009/871902871902Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary ForcesHassen M. Ouakad0Mohammad I. Younis1Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902, USADepartment of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902, USAWe 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 and geometric nonlinearities. 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.http://dx.doi.org/10.1155/2009/871902
collection DOAJ
language English
format Article
sources DOAJ
author Hassen M. Ouakad
Mohammad I. Younis
spellingShingle Hassen M. Ouakad
Mohammad I. Younis
Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary Forces
Mathematical Problems in Engineering
author_facet Hassen M. Ouakad
Mohammad I. Younis
author_sort Hassen M. Ouakad
title Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary Forces
title_short Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary Forces
title_full Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary Forces
title_fullStr Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary Forces
title_full_unstemmed Modeling and Simulations of Collapse Instabilities of Microbeams due to Capillary Forces
title_sort modeling and simulations of collapse instabilities of microbeams due to capillary forces
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2009-01-01
description 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 and geometric nonlinearities. 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.
url http://dx.doi.org/10.1155/2009/871902
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