Free vibration analysis of a rotationally restrained carbon nanotube with porozity

This study investigated the mechanical behavior of carbon-based nanotubes in various conditions. Firstly, the buckling analysis of constrained nanotubes placed in the electromagnetic field is investigated based on the Euler-Bernoulli beam theory in conjunction with Eringen's nonlocal elasticity theory. The modal displacement function is assumed for the stability analysis to discretize the derived governing equation. A detailed study is presented to demonstrate the effects of various parameters such as Hartmann parameter, spring parameter and mode number on the stability response and critical buckling load of electromagnetic nanobeam. In another part of the study, a finite element formulation is presented to analyze the free vibration of carbon nanotube-based sensors in conjunction with modified couple stress and Rayleigh beam theories. Numerical results are presented to show the frequency variation with various parameters such as the material length scale parameter, number of the finite elements, length of the nanotube and mode number. Then, the axial vibration behavior of nanotubes with different boundary conditions was investigated. Bishop's rod theory is implemented to simulate axial deflection. Size-dependency is captured by using Eringen's nonlocal elasticity theory. Based on nonlocal deformable boundary conditions and Stokes' transformation, a system of linear equations is derived and then constructed as an eigenvalue problem. Several numerical examples are presented to investigate the significance of parameters such as geometric parameters, vibrational modes, various values of the nonlocal parameter and axial spring parameters on the axial frequencies of nanotubes. Then, again using Bishop's rod theory and Eringen's nonlocal elasticity theory, this time the size-dependent free axial vibration of a nanotube made of porous material. The porous nanotube is considered in arbitrary boundary conditions and for this purpose, it is modeled with elastic springs at both ends.