Abstarct: In the last decade, carbon nanotubes have a special application in various industries due to their unique and diverse properties in the medical, electrical, oil and gas industries. Carbon nanotubes have great potential for regenerative medicine applications. Therefore, it has been very important to investigate the dynamic behavior and types of instabilities created in carbon nanotubes, which are excited by the fluid flow. In order to calculate the average and critical velocities of the passing fluid (velocities at which the nanotube loses its stability), modeling of nanotubes with different theories such as Euler-Bernoulli beam, Timoshenko beam and elastic shell model with various boundary conditions has been done. In this thesis, first, by assuming the Euler-Bernoulli beam, the pipe containing fluid flow will be modeled, then by examining the effect of Eringen's theory of non-local elasticity, the appropriate model will be obtained, then for the first time, by examining the piezoelectric effect and finding the optimal place for its installation on the nanotube, a suitable control method is chosen and the vibration of the system will be controlled. According to the results, it can be said that the fluid flow creates a following force that causes the instability of the nanotube, and the use of piezoelectric leads to stability of the nanotube.