Parametric dynamical investigation of axially graded spinning tubes conveying fluid by considering scale effects

In order to improve the performance of bi-gyroscopic systems, the vibrations and stability of an axially graded whirling nanotube containing fluid under an axial force have been studied numerically and analytically based on the nonlocal strain gradient theory. Also, a detailed parametric study has been performed to explain the effect of various key factors such as the type of material distribution and size-dependent parameters on the divergence and flatter of the system. Meanwhile, a comparative study has been performed to evaluate existing theories in the field of modeling of nanofluidic systems. It is assumed that the material characteristics of the system change according to the power-law along a longitudinal direction. To correct formulate the system, the slip condition is considered. Using the Laplace transform and the Galerkin discretization technique, the size-dependent governing equations of the system have been solved. In addition, an analytical method has been used to identify system instability thresholds. Vibrational configuration, Campbell diagrams, and system stability maps were tested, and for the first time in this paper, it is demonstrated that by adjusting correctly the axial graded of the material, the dynamic evolution process of the system can be changed. Also, it has been concluded that unlike nonlocal and density gradient parameters, by increasing the strain gradients and elastic modulus gradients, stability areas can be expanded and the destabilizing effects of compressive axial load can be reduced.