Stochastic dynamic analysis of porous functionally graded plate: A multivariate adaptive regression splines approach

This paper introduces a methodology that combines Multivariate Adaptive Regression Splines (MARS) modelling and Monte Carlo Simulation to investigate the natural frequencies of porous functionally graded material (FGM) plates along with the frequency response function (FRF) analysis. The MARS model captures the nonlinear relationship between natural frequencies and different parameters, while the FRF approach provides insights into the plate's frequency response. The proposed methodology is accurate and helpful in studying the impact of porosity, power law index, temperature, and plate thickness on the first three natural frequencies, considering the stochastic variations in material properties caused by manufacturing errors. The porous FGM plate is subjected to a traditional finite element (FE) analysis with random material properties. The power law distribution is used to ascertain the material characteristics of porous functionally graded plates. The effects of critical material characteristics, such as elastic Young's modulus, shear modulus, Poisson's ratio, and mass density, on the natural frequencies of porous FGM are examined. The results show that MARS-based finite element analysis has better computational efficiency than Monte Carlo simulations-based finite element analysis.