Abstract
This paper investigates the coupled mechanics of a fluid-conveying microtube embedded inside an elastic medium and subject to a pretension. The fluid-structure interaction model of the microsystem is developed based on Lagrange’s equations for the open system of a clamped-clamped microtube. A continuation model is used to examine the nonlinear mechanics of this microsystem prior to and beyond losing stability; the growth and the response in the supercritical regime is analysed. It is shown that the microtube stays stable prior to losing stability at the so-called critical flow velocity; beyond that point, the amplitude of the buckled microsystem grows with the velocity of the flowing fluid. The effects of different system parameters such as the linear and nonlinear stiffness coefficients of the elastic medium as well as the length-scale parameter and the slenderness ratio of the microtube on the critical speeds and the post-buckling behaviour are analysed.
Highlights
Many microelectromechanical systems (MEMS) using microscale structures such as microshells, microplates and microtubes have been designed and analysed in recent years [1,2]
Ahangar et al [13] obtained the natural frequencies of a microtube conveying fluid as a function of the fluid velocity while the microsystem is modelled based on the modified couple stress (MCS) theory [14,15,16,17,18,19]; it was shown that depending on the type of the boundary conditions, the microsystem may possess real, imaginary, or a combination of real and imaginary natural frequencies
Kural and Özkaya [20] employed the method of multiple scales to obtain the natural frequencies in the oscillation behaviour of fluid-conveying microtubes resting on an elastic bed
Summary
Many microelectromechanical systems (MEMS) using microscale structures such as microshells, microplates and microtubes have been designed and analysed in recent years [1,2]. Analysed the vibration behaviour of a cantilevered microtube in order to obtain the natural frequencies and mode functions for the transverse motion. Mashrouteh et al [30] employed the variational iteration method in order to analyse the nonlinear vibrations of fluid-conveying microtubes; the main aim was to obtain the relation between the amplitude of the transverse motion and the nonlinear natural frequency of the microsystem. This paper, for the first time, analyses the buckling and post-buckling behaviour of a fluid-conveying microtube embedded in an elastic medium by means of the MCS theory To this end, Lagrange’s equations along with as assumed-mode method are utilised to derive the equations of motion of the microsystem. Effects of different microsystem parameters, such as the flow velocity and the length scale parameter on the critical flow velocities and post-buckling behaviour are highlighted
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