Calibration of nonlocal generalized helical beam model for free vibration analysis of coiled carbon nanotubes via molecular dynamics simulations

Abstract

This paper studied the free vibration behavior of coiled carbon nanotubes (CCNTs) using continuum mechanics methods and molecular dynamics (MD) simulations. Based on the continuum mechanics method, a new elasticity model called the nonlocal generalized Washizu beam (NGWB) was innovated by considering the effects of the curvature and cross-section thickness of nanotubes, as well as size-dependent effect. Then, the governing equations for the vibrational behavior of CCNTs were derived and solved using the numerical generalized differential quadrature method (GDQM). The free vibration behavior of CCNTs was also examined by performing the MD simulations to determine the calibrated values of the nonlocal parameter ($\mu$) that are applied in the NGWB elasticity model and to validate and evaluate the obtained results. Since the NGWB elasticity model considers the size-dependent effect on the vibrational behavior, obtained results from it well agrees with the MD simulation results in the present study. For CCNTs, there was a coupling between transverse, longitudinal, and torsional vibrations, which led to the beating phenomenon. The natural frequencies decreases by increasing the number of pitches ($n_p),$ aspect ratio $(p/D),$ and pitch angle $(\overline{\alpha }).$ The nonlocal parameter has a more significant effect on the frequencies of CCNTs with smaller geometrical parameters. In addition, the type of boundary conditions affects the calibrated values of the nonlocal parameter, frequency values, and arrangement of vibrating mode shapes of CCNTs. Results of the present study can be applied in the design and analysis of nano-electro-mechanical systems (NEMS), sensors, and nano-composite structures containing CCNTs. Also, the NGWB elasticity model might be useful in the statics and wave propagation studies of CCNTs, and other coiled and curved nano-structures.

Keywords:

• Coiled carbon nanotubes
• free vibration
• nonlocal generalized Washizu beam elasticity model
• generalized differential quadrature method
• molecular dynamics simulation