Dynamic analysis of GPLs reinforced microcapsules subjected to moving micro/nanoparticles using mathematical modeling and deep-neural networks

In the realm of engineering, the use of cylindrical microcapsules containing moving micro/nanoparticles is crucial. Therefore, biomechanical engineers must focus on increasing its stability so that it may be used in a variety of scenarios. Thus far, graphene nanoplatelets, or GPLs, have shown their efficacy as an epoxy reinforcement in enhancing the material's characteristics in comparison to plain epoxy. This indicates that GPLreinforced epoxy has the potential for use as the fiber composite's matrix phase. Thus, bending data of the thick cylindrical microcapsule with GPL reinforcement under a moving load is reported in this study. A modified couple stress theory or MCST with a single length scale parameter is proposed for simulating the micro-size structure. The high-order shear deformation theory are used to represent the displacement fields while taking the shear-strain function into account. The space-dependent equations are solved using the Laplace transform approach and the double Fourier series, respectively, using forced vibration analysis. The results are compared and validated with another published study in the literature after the modeling and solution of the governing equations of the GPLs reinforced microcapsules exposed to moving micro/nano particles. With the help of the findings from the mathematical modeling section, deep neural networks (DNN) with output, input, and hidden layers are used to mimic the existing microcapsule in order to provide further verification and introduce machine learning methodologies for addressing engineering challenges. A cylindrical microcapsule under motion under a micro/nanoparticle may be modeled in the area of biomechanical engineering using the current outputs obtained from mathematical modeling and DNN sections.