Thermal–mechanical vibration and instability analysis of fluid-conveying double walled carbon nanotubes embedded in visco-elastic medium

Transverse vibration of fluid-conveying double walled carbon nanotubes (DWCNTs) embedded in biological soft tissue is studied in this paper. Based on the thermal elasticity theory, the nonlocal Euler–Bernoulli beam model is used to investigate the vibration and instability properties of the fluid-conveying DWCNTs. The biological soft tissue as a kind of visco-elastic foundation is formulated using the Kelvin–Voigt model. The results show that the resonant frequencies and the critical flow velocity at which structural instability occurs are significantly depended on the properties of the surrounding medium, the boundary conditions, the nonlocal parameter and the temperature change. The nonlocal parameter plays an obvious effect on the second mode resonant frequency. Three typical boundary conditions as clamped–clamped, clamped–pinned and pinned–pinned are used to illustrate the effects of the boundary conditions. The damping parameter of the visco-elastic foundation causes an obvious reduction of the critical flow velocity. Furthermore, the increase of temperature change reduces the effect of visco-elastic medium on the critical flow velocity.