Axial dynamic buckling analysis of embedded single-walled carbon nanotube by complex structure-preserving method

The occurrence of the axial dynamic buckling in the carbon nanotube may cause the failure of some nano-sensors, which is difficult to be investigated by the experimental approach for the rigorous measuring accuracy requirement. Thus, a complex structure-preserving method is proposed to investigate the axial dynamic buckling properties of an embedded single-walled carbon nanotube in this paper. The nonlocal Euler-Bernoulli beam model of the embedded single-walled carbon nanotube under a concentrated excitation with a small included angle in the acting direction of the excitation against the cross-section of the carbon nanotube is presented. Introducing several intermediate variables, the multi-symplectic form of the oscillation model is obtained, which is a structure-preserving order-reduce process. To investigate the axial dynamic buckling of the carbon nanotube numerically with an acceptable step length, a complex structure-preserving method that combines the precise integration method for the grids near the acting position of the excitation and the Preissman multi-symplectic scheme for other grids is proposed. Considering two typical excitations, the oscillation of the carbon nanotube is simulated by the complex structure-preserving method and the axial dynamic buckling properties of the nanotube are investigated. From the numerical results, it can be concluded that the axial dynamic buckling phenomenon in the carbon nanotube is more likely to occur when the included angle increase or the frequency of the excitation is close to MHz with the given parameters, which gives guidance for the design of the excitation of the nano-oscillator.