Free vibration and nonlinear transient analysis of blast-loaded FGM sandwich plates with stepped face sheets: Analytical and artificial neural network approaches

This study investigates the free vibration and transient dynamic response of functionally graded material (FGM) sandwich plates with stepped face sheets (FGM-SPSFS) supported by viscoelastic foundation under blast loading. The research focuses on the effects of geometric configurations and material property variations across segments. Each plate comprises three layers: a homogeneous hard core and two FGM face sheets, divided horizontally into two segments with differing face sheet thicknesses, which enhance structural stiffness while maintaining a consistent total thickness. The material properties of the sandwich plates follow a power-law distribution. The formulations are based on higher-order shear deformation plate theory and von Kármán geometric nonlinearity, and are solved using Galerkin's method. Validation is achieved by comparing the results with published literature and finite element analysis (FEA). Artificial neural network (ANN) models are developed to predict natural frequencies without extensive computational runs, employing Bayesian Regularization (BR) and Levenberg–Marquardt (LM) algorithms in MATLAB. A new graphical user interface (GUI) tool facilitates frequency predictions using the proposed ANN model. Key findings indicate that modifications to the stepped face sheets and core layers affect stiffness, natural frequency, and vibration amplitudes. Increasing the core-to-total thickness ratio enhances stiffness, resulting in higher frequencies and reduced displacement amplitudes. The LM algorithm outperforms the BR algorithm, with errors generally below 1%, compared to 2% to 4% for BR with the log-sigmoid function. This study offers valuable insights into the design and analysis of FGM sandwich structures for engineering applications.