Abstract
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.
Highlights
The objective of this paper is to provide an analytical method to calculate the coupled frequencies of vibration of microbeams partially immersed in a viscous fluid
Reference [16] uses finite element analysis (FEA) method in order to predict the dynamic response of the cantilever beam
For coupled vibration analysis of beams partially immersed in a viscous fluid, the accuracy of the present method has been compared with the results obtained with
Summary
The objective of this paper is to provide an analytical method to calculate the coupled frequencies of vibration of microbeams partially immersed in a viscous fluid. The motivation of this work is to provide a theoretical model that can be used in the design and interpretation of density and viscosity sensors. Due to their size and potential for highly sensitive and low cost compact device applications, microstructures are becoming increasingly attractive for sensing applications and have been studied extensively in recent years. A precise modeling of the solid-fluid interaction and the determination of the frequency response enable the measurement of the density and the rheological behavior of fluids [11,12,13,14,15,16]. Reference [16] uses finite element analysis (FEA) method in order to predict the dynamic response of the cantilever beam
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