| Abstract: | The nonlinear free vibration of non-prismatic single-walled carbon nanotubes (SWNTs) is studied using a new non-local shear deformable beam p-element. The effects of the internal length scale parameter, transverse shear deformation, rotary inertia, and geometrical nonlinearity are taken into account. The principle of virtual displacements and the harmonic balance method are used to derive the nonlinear equations of motion, which are solved iteratively by the linearized updated mode method to obtain the fundamental nonlinear frequencies and mode shapes of H–H, C–H, and C–C SWNTs with uniform, linear, and quadratic radius variation. The convergence and accuracy of the non-local shear deformable beam p-element are demonstrated through comparison with other methods. It is shown that the non-uniformity parameters influence significantly the backbone curves and mode shapes of non-prismatic SWNTs. |
