A new formulation to study in-plane vibration of curved carbon nanotubes conveying viscous fluid

Shortly after the discovery of carbon nanotubes (CNTs), the existence of differently shaped CNTs other than straight ones was predicted theoretically. Recently photomicrographic images show that CNTs are not actually straight but have significant curvature. This aspect was mostly neglected in previous studies on CNTs’ dynamic behavior. In this paper a new formulation governing the in-plane motion of curved CNTs conveying viscous fluid is derived to study their in-plane free vibration. In this formulation the fluid is considered to be viscous and the size effects of nanotubes are also taken into consideration through nonlocal elasticity theory. In this study CNT is modeled as a hollow cylindrical tube and the moving fluid inside is modeled as a plug flow characterized by its mass density, viscosity, and mean velocity. The new formulation is used to study the vibration and instability characteristics of curved and wavy carbon nanotubes. Using finite element analysis it is shown that the nonlocal parameter, the viscosity of fluid, and also the curvature have considerable effects on the natural frequency and critical flow velocity of carbon nanotubes. Also the effect of boundary conditions on natural frequency and critical flow velocity is studied.