Nonlocal excitation and potential instability of embedded slender and stocky single-walled carbon nanotubes under harmonically vibrated matrix

Until now various aspects of vibrations of single-walled carbon nanotubes (SWCNTs) have been explored; however, their dynamics and possible instabilities because of the excitation of matrix have not been addressed methodically. By considering a harmonic transverse excitation, the explicit expressions of elastic fields are obtained based on the nonlocal Rayleigh, Timoshenko, and higher-order beam models. The roles of the nonlocality, slenderness ratio, amplitude and frequency of matrix excitation and interactional behavior of the embedded nanotube on the dynamic transverse displacements of SWCNTs are comprehensively displayed. The capabilities of the Rayleigh model as well as the Timoshenko model in capturing the deflection of the nanostructure based on the higher-order beam theory are also explained in some detail. The nonlocal elastodynamic fields of the nanostructure in the resonance state as well as the critical values of lateral and rotational stiffness of the matrix are also introduced and the influences of crucial factors on such parameters are explained and discussed carefully.