Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation

Carbon nanotubes (CNTs) are used for a variety of technological and biomedical applications. Fluid flows inside CNTs have become an attractive research topic in recent years. In the present study, the vibration and instability analysis of a CNT resting on a linear viscoelastic Winkler foundation are investigated based on the classical Euler–Bernoulli beam model. The effect of internal moving fluid is characterized by two parameters, the steady flow velocity and the mass density of the fluid. The finite element method is used to discretize the equation of motion, and the resonant frequencies are obtained by solving a quadratic eigenvalue problem. The lowest four frequencies are determined for different boundary conditions. The effects of the modulus and the damping factor of the linear viscoelastic Winkler foundation and the fluid velocity on the resonance frequencies are also examined. The validity of the present analysis is confirmed by comparing the results with those obtained from the literature.