Computational investigation of size-dependent vibrational behavior in two-dimensional nanomaterial-reinforced composites

This study investigates the vibrational behavior of carbon nanosheet-reinforced polymer nanocomposites using a multiscale finite element modeling approach. The carbon nanosheets are represented using beam elements calibrated to molecular mechanics parameters, while the polymer matrix is treated as a continuum medium. Non-bonded van der Waals interactions at the nanosheet–matrix interface are modeled using spring elements derived from the Lennard-Jones potential. The model is validated by comparing predicted Young’s modulus values with theoretical and experimental results from the literature, showing good agreement. The influence of nanosheet geometry, chirality, volume fraction, and boundary conditions on the natural frequencies of the nanocomposite is systematically analyzed. The results indicate that increasing the aspect ratio from 1 to 5 reduces the natural frequency by 76%–82% for armchair nanosheets under clamped-free boundary conditions. At volume fractions below 8%, frequency increases monotonically with concentration; however, at 11% volume fraction and aspect ratios exceeding 2, frequency improvements diminish by 15%–20% relative to the 5% case, suggesting agglomeration-induced stiffness degradation. Armchair nanosheets exhibit 5%–8% higher natural frequencies than zigzag configurations across all geometries tested. In addition, armchair nanosheets consistently exhibit higher natural frequencies than zigzag configurations, highlighting the role of atomic orientation in mechanical performance. The findings provide insights into optimizing nanosheet geometry and dispersion for applications requiring enhanced vibrational characteristics, such as nano-resonators and mechanical sensors. This work offers a comprehensive framework for understanding and tailoring the dynamic response of two-dimensional nanomaterial-reinforced composites.