Thermo-electro-magneto-mechanical vibration and machine learning based multi-objective optimization of MWCNT/GNP hybrid sandwich plate with auxetic honeycomb core

Abstract

Nanocomposites reinforced with multi-walled carbon nanotubes (MWCNTs) or graphene nanoplatelets (GNPs) have been widely studied due to their enhanced mechanical, thermal and electrical properties; however, hybrid systems combining both nanofillers remain relatively underexplored, particularly in sandwich structures with multifunctional materials. To address this gap, the vibration behaviors and multi-objective optimization of sandwich plate comprising auxetic honeycomb core, two hybrid nanocomposite intermediate layers reinforced with MWCNTs and GNPs and two magneto–electro–elastic (MEE) face sheets are investigated. Four different distribution patterns of CNTs and GNPs, namely O, X, U and V are considered. The governing equations are formulated based on Reddy’s higher order shear deformation plate theory, incorporating von Kármán nonlinear strain–displacement relationships. Various parametric studies are performed to examine the effects of the weight fractions and distribution patterns of CNTs and GNPs, MWCNT:GNP distribution ratio, GNP size, temperature increment, viscoelastic foundations as well as geometrical parameters. For the optimization problem, to reduce the computational cost of repeated analytical evaluations, six machine learning (ML) models are used to construct surrogate models integrated into the non-dominated sorting genetic algorithm II (NSGA-II) to simultaneously maximize the natural frequency and minimize the mass of the sandwich plate. The results demonstrate that the pure GNP reinforcement provides superior stiffness, whereas the balanced MWCNT:GNP ratio of 1:1 offers higher stiffness than the other hybrid reinforcement configurations and the pure CNT reinforcement exhibits the lowest stiffness. Furthermore, the integration of ML models into NSGA-II preserves the quality of the obtained solutions while reducing the computational cost by approximately 88.31–92.63%.