Abstarct: This thesis is aimed to investigate the nonlinear vibration of a double walled carbon nanotube conveying fluid, covered by a piezoelectric laxyer, and embedded in a viscous fluid. In this analysis, an Euler-Bernoulli beam model is used and in order to considering of size dependent effects, nonlocal theories is implemented. The governing equations of motion are derived using Hamilton’s principle and then, the Galerkin procedure and the multiple scales method is used to solve the equitions and investigate the vibration behavior of the system. It is receivable from this analysis that increasing the thickness of external fluid causes to increase the stability of the system. Also additional increase in thickness beyond a critical value causes no effect on vibration behavior of the system.