A size effect parameter-calibrated strain gradient theory (SGT) model for vibrational analysis of the graphyne using atomistic simulations

Graphyne is one of the new carbon allotropes, and its structures have interesting mechanical, electrical, and thermal properties due to their unique geometry. In this research, the vibration behavior of graphyne structure consists of axisymmetric and asymmetric vibrational modes are studied using a combination of strain gradient theory and molecular dynamics simulations (hybrid model of strain gradient-molecular dynamics simulations). Using the molecular dynamics simulation method to calculate graphyne's first four resonance frequencies under dynamic loading. Strain gradient theory is applied to determine the nonlocal effects of this structure. A crucial issue when applying non-classical continuum models is the calibration of the size effect parameter. According to strain gradient theory, the size effect parameter can be obtained using the results of modal analysis from atomic simulations compared to those of continuum mechanics theories. Our approach to calibrating size parameters is based on optimization methods such as genetic algorithm optimization. The effects of diameter and mode on the resonance frequencies and size parameters are analyzed separately and in detail. Based on the results, it is evident that the lowest amount of error occurs when the size parameter is a function of diameter and vibration mode. The biggest error occurs when the size parameter is assumed to be a constant for each vibration mode and diameter.