An Analytical Investigation on Nonlinear Vibrations of Timoshenko Nanotubes Conveying Flow Based on Stress Driven-Nonlocal Theory Considering Nonlinear Foundation, Magnetic Field and Thermal Effects

This study examines the combined effects of magnetic fields, temperature change, and nonlocal elasticity on the nonlinear vibration behavior of nanotubes conveying fluid flow. The analysis is based on Timoshenko beam theory, which accounts for rotational inertia and shear deformation, together with the stress-driven nonlocal theory. The governing equations of the nanotube resting on nonlinear elastic foundations considering the thermomagnetic effects are derived using the Von-Kármán strain relations in conjunction with Hamilton’s principle. These equations are reduced to a set of nonlinear ordinary differential equations via the Galerkin method. The resulting time-dependent system of nonlinear equations are then solved analytically using homotopy analysis method for the first time, yielding closed-form expressions for both the nonlinear frequency and time-domain response. A comprehensive parametric study is conducted to explore the influence of various physical and material parameters on the system’s vibrational characteristics. The findings indicate that increases in magnetic field strength, temperature change, or slenderness ratio lead to a reduction in the nonlinear frequency ratio. Additionally, both the fluid velocity and fluid density decrease the nonlinear frequency but the initial amplitude leads to increase it.