Flow induced bifurcation and phase-plane stability analysis of branched nanotubes resting on two parameter foundation in a magnetic environment

Abstract

This paper explores the nonlinear partial differential equations (PDEs) for transverse and longitudinal vibrations of slightly curved fluid-conveying embedded branched nanotubes operating in a magnetic environment. Using Bernoulli–Euler, Nonlocal and Hamilton theories, equations of motion governing the vibrations of the nanotubes are developed. Thereafter, the developed inimitable equations are solved using the numerical PDE solver and PDE-tool in MATLAB. With the numerical solutions, visualizations and parametric studies were carried out. The results indicate that increasing the branch angle at the downstream decreases quantitative stability. Furthermore, the stability results acquired via simulation point out that the magnetic field has a damping or attenuating influence of about 20%. The solutions as presented in this study match with existing results from previous studies, hence the verifications and validations of this work. It is envisioned that the results obtained will provide better physical insights into the stability criteria for carbon nanotubes and will enhance the designs of nanomechanical carbon nanotubes-based devices that convey fluid and operate in elastic and magnetic environments.