Characterizing the nonlinear behaviour of double walled carbon nanotube based nano mass sensor

This work deals with the evaluation of nonlinear behaviour of a curved double walled carbon nanotube (DWCNT) when used for mass sensing applications. The DWCNT is considered to be doubly clamped at a source and a drain. To judge the nonlinear behaviour, equations of motion have been derived using Euler beam theory and Hamilton principle, considering nonlinear van der Waals interaction nonlinear oscillations of a double walled carbon nanotube excited harmonically near its primary resonance are considered. The nonlinear free vibration of double-walled carbon nanotubes based on the elasticity theory is studied in this paper. Modelling of the weak van der Waals force of attraction between the inner and outer tubes is represented using a spring element. The equation of motion involves four nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the double walled carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass, inner and outer tubes and the geometric imperfections of double walled carbon nanotube.