Recently, carbon nano-tubes (CNTs) have drawn a great deal of attention, because CNTs have potential usage as cancer therapy devices or nano-vessels for conveying and storing fluids and drug delivery in medicine and bio-nanotechnology. In this regard a remarkable number of studies have been accomplished to disclose the vibrational behavior and stability responses of such nano-structures subjected to fluid flow. Several researchers have utilized various theories such as Euler-Bernoulli and Timoshenko beam models, and elastic shell structure with different boundary conditions for investigating the critical mean flow velocity of CNT conveying fluid. In this dissertation, we would model the CNT by both Euler-Bernoulli and shallow shell Donnell. We would utilize Galerkin weighted residual method for discretizing the governing fluid-structure interaction (FSI) equations. For analyzing the dynamic response of CNT more accurately, we would investigate the size effects of nano-structure by using nonlocal and strain/inertia gradient theories. We would observe that the nonlocal continuum theory could suggest that the pipe conveying fluid could lose its stability sooner and the critical velocity and eigen-frequencies would be smaller than that of justify; MARGIN: 0cm 0cm 0pt" In addition, we would reappraise the well-known equation of motion for a pipe conveying viscous fluid. We would reveal that the viscosity of the fluid flow should not appear explicitly in the equation of motion of Euler-Bernoulli conveying fluid. Besides, we would develop a FSI model for shallow shell Donnell conveying irrotational and viscous flow. Finally, we would compare the results obtained by Galerkin and wave traveling methods. Keywords: fluid-structure interaction; divergence and flutter instabilities; Euler-Bernoulli beam; Donnell shallow shell; nonlocal theory of Eringen; strain/inertia gradient theory; slip flow regime; viscosity.
