Nonlocal Thermal–Mechanical Vibration of Spinning Functionally Graded Nanotubes Conveying Fluid Based on the Timoshenko Model

Based on the Timoshenko beam theory, this paper proposes a nonlocal bi-gyroscopic model for spinning functionally graded (FG) nanotubes conveying fluid, and the thermal–mechanical vibration and stability of such composite nanostructures under small scale, rotor, and temperature coupling effects are investigated. The nanotube is composed of functionally graded materials (FGMs), and different volume fraction functions are utilized to control the distribution of material properties. Eringen’s nonlocal elasticity theory and Hamilton’s principle are applied for dynamical modeling, and the forward and backward precession frequencies as well as 3D mode configurations of the nanotube are obtained. By conducting dimensionless analysis, it is found that compared to the Timoshenko nano-beam model, the conventional Euler–Bernoulli (E-B) model holds the same flutter frequency in the supercritical region, while it usually overestimates the higher-order precession frequencies. The nonlocal, thermal, and flowing effects all can lead to buckling or different kinds of coupled flutter in the system. The material distribution of the P-type FGM nanotube can also induce coupled flutter, while that of the S-type FGM nanotube has no impact on the stability of the system. This paper is expected to provide a theoretical foundation for the design of motional composite nanodevices.