Thermo-mechanical vibration and stability behaviors of bi-directional FG nano-pipe conveying fluid

Abstract

This work focuses on the thermo-mechanical modeling of a size-dependent pipe made of bi-directional functionally graded (FG) materials and conveying fluid through its inner wall. The material properties of this FG nano-scale pipe along radial and axial directions are assumed to be separately varying according to the power-law and exponential distributions. The governing equations of the FG nano-scale pipe are derived according to nonlocal strain gradient theory and Hamilton’s principle, and interactions between the size-dependent pipe and its inner fluid are revealed via size-dependent constitutive relation. The frequency response of the pipe and its critical flow velocity are calculated via generalized differential quadrature method. After validation of the proposed model by comparing with previous works, a detailed parametric study is conducted to fully examine the coupling effect of material distribution and various parameters including small size, aspect ratio, boundary constraint, temperature change and flow velocity on the frequency response of the FG nano-pipe. Simultaneously, the critical flow velocity of inner fluid under which the divergence phenomenon appears is also predicted and physically explained in detail. Numerical results show that bi-directional FG design is especially beneficial to improve the stability of FG nano-pipe, which can provide a guide to design advanced micro/nanofluidic devices for bio-engineering applications.