The applicability of nonlocal shear deformation theory and scale parameters for guided wave propagation in nanoplates

This paper aims to explore the applicability of the Kirchhoff plate, Mindlin plate, second-order shear deformation plate, and third-order shear deformation plate models in predicting and explaining the micro/nanoscale structures of wave behavior in the context of nonlocal elasticity theory. Based on the molecular dynamics simulation results, the nonlocal parameters of shear deformation plate models and three-dimensional plate models are calibrated by neural network and root mean square error. The research results show that the results of molecular dynamics simulation are very consistent with the solution of the three-dimensional plate model with the calibrated nonlocal parameters, which are 0.0762 nm and 0.0776 nm for A0 and S0 modes of the Lamb wave, 0.1825 nm and 0.174 nm for SH0 and SH1 modes of the SH wave. Due to the more complex atomic vibrations involved in the propagation of Lamb waves compared to SH waves, the difference in nonlocal parameters between A0 and S0 modes is significantly larger than that between SH1 and SH0 modes. Furthermore, the simplified plate model exhibits larger nonlocal parameter values for A0 and S0 modes compared to the three-dimensional plate model. For the simplified model with calibrated nonlocal parameters, its Lamb wave solutions are consistent with the results of molecular dynamics at low dispersion regions, while the error is larger at severe dispersion regions. Conversely, the results of SH waves and molecular dynamics always show good consistency. Based on a comprehensive consideration of the scope of the application, the most suitable model can be selected within the allowable range of errors to describe and analyze the wave behavior of a specific structure within a certain frequency range.