Table of Contents
Physics Research International
Volume 2016 (2016), Article ID 6761372, 14 pages
Research Article

Vibration Analysis of Euler-Bernoulli Beams Partially Immersed in a Viscous Fluid

1Arts et Métiers ParisTech, ENSAM Angers, 2 boulevard du Ronceray, 49035 Angers, France
2IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France

Received 17 September 2015; Revised 20 January 2016; Accepted 27 January 2016

Academic Editor: Israel Felner

Copyright © 2016 Wafik Abassi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The vibrational characteristics of a microbeam are well known to strongly depend on the fluid in which the beam is immersed. In this paper, we present a detailed theoretical study of the modal analysis of microbeams partially immersed in a viscous fluid. A fixed-free microbeam vibrating in a viscous fluid is modeled using the Euler-Bernoulli equation for the beams. The unsteady Stokes equations are solved using a Helmholtz decomposition technique in a two-dimensional plane containing the microbeams cross sections. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results is compared with present method for validation and an acceptable match between them was obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy.