Vibrational characteristics of single-walled carbon-nanotube: Time and frequency domain analysis

Abstract

In this paper, the vibrational characteristics of higher modes of single-walled carbon-nanotube (SWNT) modeled as the continuum axisymmetric cylinder are studied in both time and frequency domains. The modeling of SWNT for the high frequency dynamic analysis is done using the wavelet based spectral element method and this numerical technique involves the Daubechies scaling function approximation in time and one spatial (axial) dimension. This model is capable of capturing the coupled longitudinal-radial vibration arising due to the finiteness of SWNT. Here, first the phonon dispersion relation is obtained and validated with the atomistic and other continuum model simulations available. The effects of dimensional parameters on higher radial, longitudinal, and coupled radial-longitudinal vibrational modes are studied. Dependence of the higher mode frequencies on these parameters are much different from that of the first mode frequencies. Further time domain responses for broadband excitations are simulated and effects of the radius and thickness of the SWNT are studied. The prominent influence of the above geometrical parameters are observed in the time domain results.