Size-dependent vibration and instability of simply supported microtubes conveying fluid embedded in elastic medium

In this study, size-dependent vibration and instability of a simply supported microtube conveying fluid embedded in elastic medium is investigated based on modified couple stress theory. A Winkler-type foundation is employed to model the interaction between microtube and the surrounding medium. The governing equation is derived by a combination of the basis equation of modified couple stress theory and Hamilton's principle. The critical flow velocity is calculated by an analytically method based on classicalsolution. The Galerkin method is used to discretize the equation of motion, then frequencies of microtube conveying fluid is obtained by solving a quadratic eigenvalue problem. For a simply supported microtube conveying fluid, the natural frequencies decrease with increasing flow velocity and microtube loses stability by divergence or a pitchfork bifurcation (buckling) at the critical flow velocity. More significantly, when the outside diameter of micro pipe is comparable to the material length scale parameter, the frequencies and critical flow velocities predicted based on non-classical (modified couple stress) theory is higher than those predicted by classical theory. Elastic medium enhance the stability of microtube, however, when the stiffness of elastic medium increases the differences between two theories decrease and then increase and this procedure repeats. The reason of such behavior is the mode destabilizes the system, due to the stiffness of elastic medium and material length scale parameter.

Keywords:

Size Dependency , Vibration and Instability , Simply Supported Microtube Conveying Fluid , Elastic Medium , Modified Couple Stress Theory