Dynamic response of sigmoidal FGM plates with attached mass: Finite element analysis and GPR-based sensitivity assessment

Functionally graded material (FGM) plates are widely used in aerospace, marine, nuclear and civil engineering applications due to their customisable material properties. In practical structures, such plates often carry attached mass in the form of functional components; however, the combined effect of material gradation, attached mass, and plate geometry on dynamic behaviour remains insufficiently explored. In this study, the free vibration and transient response of sigmoidal skew FGM plates carrying attached mass are investigated using a third-order shear deformation theory-based finite element formulation. The plate domain is discretized using a rapidly convergent nine-node isoparametric element. Newmark’s time integration scheme is employed for transient analysis. The results reveal a strong coupling between geometric configuration and attached mass, with frequency reductions reaching up to 71% for a mass ratio of unity at large skew angles, compared to only 54% at small skew angles. Transient response analysis further shows that the presence of attached mass increases the peak deflection and vibration period, particularly when the mass is located in dynamically active regions of the plate. In addition to parametric analysis, uncertainty quantification and data-driven sensitivity analyses are performed. A Gaussian process regression (GPR)-based permutation feature importance approach (PFI) is employed to identify influential parameters. The results indicate that the mass ratio, attachment size ratio, and location have significantly higher influence on vibration characteristics than the material gradient index within the investigated range. This study provides useful insights into the vibration behaviour and parameter sensitivity of FGM plates carrying attached masses.