Magneto-thermal primary frequency response analysis of carbon nanotube considering surface effect under different boundary conditions

Present study is devoted to study the nonlinear frequency response of single walled carbon nanotubes, SWCNTs, in the case of primary resonance. Based on the nonlocal Euler-Bernoulli beam theory, the nonlinear geometry, magneto-thermal field, residual stress and surface effects on the governing equation of system are taken into account. The Galerkin technique on the basis of trigonometric mode shape functions and multiple scales method are used to solve the nonlinear governing equations. The effects of the different boundary conditions including the simply supported at two ends, S-S, clamped-clamped, C-C and clamped-simply supported, C-S, longitudinal magnetic field, amplitude of excitation, detuning parameter and surface elasticity on the nonlinear primary frequency response are analytically investigated and discussed.