Machine learning based probabilistic model for free vibration analysis of functionally graded graphene nanoplatelets reinforced porous plates

Abstract

In the present study, the machine learning based probabilistic model is proposed to perform the vibration analysis of functionally graded (FG) porous plates reinforced with graphene nanoplatelets (GNP). The plate is considered with the statistical variation in material properties such as elastic moduli of metal matrix and GNP, porosity index, and weight fraction of GNP while sampling via normal distribution. The effective material properties, i.e. elastic modulus and density of the GNP reinforced porous composite are respectively obtained using Halpin-Tsai and the rule of mixture models. The size and pore density are varied along the thickness direction using continuous cosine functions. The equation of motion based on higher-order shear deformable theory (HSDT) is derived using the variational principle which is further simulated by employing the finite element method (FEM) to obtain natural frequency. The database is generated based on selective input features and natural frequency i.e. output, and is further divided into 70% training dataset and 30% for testing and validation. A regression-based artificial neural network (ANN) model is adopted to learn the underlying function that maps the natural frequency to the inputs. The mapped model is further coupled with Monte Carlo simulation (MCS) to efficiently find the statistical variation in the natural frequency concerning variation in material properties (inputs) at reduced cost and time.