Nonlocal effects in modal analysis of forced responses with single carbon nanotubes

This paper studies forced responses of a nonlocal Euler–Bernoulli microcantilever for single carbon nanotubes which can also be employed as a tip attached to an AFM probe. Modal analysis can be used in terms of the normal mode property with single carbon nanotubes that share clamped, fixed or sliding end conditions. The modal analysis of the flexural vibrations with such boundary conditions is formulated in terms of a fundamental spatial amplitude response. Forced responses are determined through convolution with the impulse response of a beam subject to internal and external damping. This later response is systematically employed for identifying induced transients due to permanent responses. By approximating the impulse response with the Galerkin method, we have obtained closed-form forced responses due to concentrated harmonic loads and to modulated spatial finite span pulses.

► Forced single carbon nanotubes though convolution with the impulse response. ► Nonlocal modal analysis. ► Induced free vibrations reconstructed with the initial values of permanent responses. ► Galerkin approximation of the impulse response and transfer function. ► Method can handle both external and internal damping.