Faezeh Tamaskani Esfehankalateh, Mohammad Shamekhi Amiri, Hossein Pahlavan, Azizollah Ardeshir‐Behrestaghi, Timon Rabczuk, Hossein Bisheh
This paper presents a three-dimensional elasticity-based model for the free vibration analysis of a circular multilayered plate with arbitrary thickness ratio and relying on surface circumferential support, applicable to transversely isotropic functionally graded multiscale hybrid nanocomposites (MSHNC). A two-step homogenization scheme, enhanced by two parameters, is employed to capture the effects of nanoreinforcement phase agglomeration in modelling the transversely isotropic MSHNC. A layerwise approach is used to model the effects of non-uniform MSHNC feature distribution through the plate thickness, including agglomeration. The governing equations are decoupled and solved using the displacement potential function (DPF) and separation of variables methods, ensuring that the support conditions are consistently met across the boundary. The frequency equation of the plate is derived by enforcing stress-free boundary conditions together with perfect interlayer continuity conditions, using a matrix approach. Frequencies, mode shapes, and nodal patterns are illustrated through benchmark examples, together with a parametric study on the non-uniformity of plate parameters. The proposed model is validated against 3D numerical simulations in ABAQUS, confirming its accuracy and efficiency. The results reveal a notable sensitivity of laminated MSHNC circular plate responses to variations in their characteristics, particularly for larger thickness ratios and higher-order modes.