Nonlinear free and forced vibrations of curved single walled carbon nanotube on a Pasternak elastic foundation

Abstract

Based on elastic continuum mechanics, the nonlinear free and forced vibrations of an embedded single-walled carbon nanotube with waviness along its axis were analyzed. The single-walled carbon nanotube was embedded in a Pasternak elastic foundation. Two analytical approaches were utilized to obtain the frequency-amplitude relationship of the free vibrational model, and one other analytical approach was used to obtain the forced vibrations of the curved single-walled carbon nanotube on the Pasternak elastic foundation. Subsequently, a parametric study was performed to study the importance of di erent parameters, such as the amplitude of oscillation and the curvature radius, on the nonlinear behavior of the system. Also, a numerical simulation was carried out to obtain the results and investigate the accuracy of the analytical solution methods. Comparison of the results obtained by the proposed methods shows excellent agreement with those obtained by the numerical solution.