Spectral element based model for wave propagation analysis in multi-wall carbon nanotubes

A spectrally formulated finite element is developed to study elastic waves in carbon nanotubes (CNT), where the frequency content of the exciting signal is at terahertz level. A multi-walled nanotube (MWNT) is modelled as an assemblage of Euler–Bernoulli beams connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the nanotubes. The spectral element is developed using the recently developed formulation strategy based on the solution of polynomial eigenvalue problem (PEP). A single element can model a MWNT with any number of walls. Studies are carried out to investigate the effect of the number of walls on the spectrum and dispersion relation. Effect of the number of walls on the frequency response function is investigated. Response of MWNT for terahertz level loading is analyzed for broad-band shear pulse.