Primary resonance analysis of a curved single walled carbon nanotubes on the viscoelastic medium in thermal environment under harmonic force

In this paper based on the Euler-Bernoulli beam model, the primary resonance a curved single carbon nanotube subjected to axial thermal force in the case of low temperature and high temperature and resting on a viscoelastic foundation is analytically investigated. The nonlinear partial differential governing equation is reduced to nonlinear ordinary differential governing equation by using of a single-mode Galerkin approximation along with the sinusoidal curvature for clamped-clamped single walled carbon nanotube under harmonic external force. The method of multiple scales is applied to determine the analytical primary resonance frequency response. Considering the curved geometry and the mid-plane stretching, a quadratic and cubic terms are presented in the governing equation. The effects of temperature change in high temperature and low temperature conditions, viscoelastic coefficients of medium, amplitude of sinusoidal curvature and excitation amplitude are investigated to study the property frequency response and development or elimination of forward and backward jumping phenomenon in primary resonance frequency response. The results show that these parameters have a significant effect on the frequency response of a curved single walled carbon nanaotubes under transvers harmonic force.