Microfluid-induced vibration and stability of structures modeled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory

Abstract

The problem of microfluid-induced vibration and instability in the walls of the micro-channels containing internal fluid is now of considerable interest for potential micro-fluidics device applications. In this article, we have studied a non-viscous and incompressible fluid through microstructures. Based on a modified couple stress theory, a non-classical Timoshenko beam model is developed for the free vibration of microstructures containing internal fluid flow, modeled as micromachined pipes conveying fluid. Compared with the classical pipe models, this new model contains a material length scale parameter which can describe the microstructure-dependent vibration characteristics of the microscale pipes. By considering the effect of the microfluid flow, the equations of motion are derived using Hamiltonian approach. Based on the newly developed Timoshenko model, the effects of material length scale parameter and Poisson ratio on the vibration characteristics and the critical flow velocity are discussed. When the outside diameter of the pipe becomes comparable to the material length scale parameter, it is found that the natural frequencies increase remarkably and that the critical flow velocities predicted by the non-classical Timoshenko beam theory are much higher than that predicted by the classical beam theory. The size effects, however, are almost diminishing as the diameter of the pipe is far greater than the material length scale parameter. This study might be helpful to characterize the dynamical behavior of microscale pipes conveying fluid or design microfluidic and nanofluidic devices in a wide range of applications.Keywords Microscale pipes conveying fluid Á Vibration Á Non-classical Timoshenko beam model Á Size effect Á Microfluidic device 1 Introduction

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