Instability analysis and free vibration of axially moving bidirectional functionally graded Reddy plates

This study investigates the structural dynamics and vibrational stability of axially moving plates composed of two-dimensional functionally graded material (2D-FGM), where properties vary along both longitudinal and transverse directions. Using Higher-Order Shear Deformation Theory (HSDT) and Hamilton’s Principle, governing equations are derived to capture the plate’s dynamic behavior under axial motion, including gyroscopic and axial-bending couplings that critically influence stability. Natural frequencies and complex eigenvalue maps are computed via the Generalized Differential Quadrature Method (GDQM) to identify critical speeds at which divergence or mode-coalescence flutter arises. A parametric study quantifies how bidirectional power-law gradation (α,β) systematically decreases the effective stiffness-to-mass ratio and accelerates instability; this mechanistic link is shown quantitatively. To indicate methodological advances, a Physics-Informed Neural Network (PINN) framework is implemented as a proof-of-concept: (i) a forward PINN reconstructs mode shapes from the governing PDEs and boundary conditions (BCs), and (ii) an inverse PINN (I-PINN) identifies natural frequencies from sparse GDQM samples while illustrating robustness to initialization. Together, the GDQM results and PINN demonstrations advance both the physical understanding of 2D-FGM plate stability and the development of physics-constrained inverse/surrogate tools for parametric structural dynamics.