Nonlinear Thermal-Magneto-Mechanical Vibration Analysis of Single-Walled Embedded Branched Carbon Nanotubes Conveying Nanofluid

In this present study, the nonlinear thermal-magneto-mechanical stability and vibration of branched nanotube conveying nano-magnetic fluid embedded in linear and nonlinear elastic foundations are analyzed. The governing equations are established via Euler–Bernoulli theory, Hamilton’s principle, and the nonlocal theory of elasticity. The fluid flow and thermal behaviors of the nanofluid are described using modified Navier–Stokes and conservation of energy equations. With the aid of the Galerkin decomposition technique and differential transformation method (DTM), the coupled thermos-fluidic-vibration equation is solved analytically. The analytical solutions as presented in this study match with an existing experimental result and as such used to explore the influences of nonlocal parameters, downstream or branch angle, temperature, magnetic effect, fluid velocity, foundation parameters, and end conditions on vibrations of the nanotube. The results indicate that decreasing temperature change and augmenting the nanotube branch angle decreases the stability for the prebifurcation domain but increases for the post-bifurcation region. Furthermore, the magnetic term possesses a damping or an attenuating impact on the nanotube vibration response at any mode and for any boundary condition considered. It is anticipated that the outcome of this present study will find applications in the strategic optimization of designed nano-devices under thermo-mechanical flow-induced vibration.