Transient dynamic analysis of two-directionally functionally graded rotating disks under instantaneous force

This study conducts a comprehensive analysis of the transient dynamic behavior of two-directionally (2D) functionally graded (FG) rotating brake disks subjected to instantaneous braking forces. The disk is composed of a temperature-dependent mixture of ceramic (Al₂O₃) and metallic (Gray Cast Iron [GCI]) phases, with material properties varying continuously in both the radial and thickness directions to reflect real-world manufacturing gradients. A sudden braking force is applied at the disk's outer surface, simulating emergency braking scenarios commonly encountered in automotive systems. To accurately capture the mechanical and thermal response, advanced theoretical models – namely, the quasi-3D refined plate theory and refined zigzag theory – are utilized. These theories incorporate transverse shear deformation without the need for shear correction factors, enabling enhanced prediction accuracy. The governing partial differential equations are formulated using the variational energy method and are discretized spatially via the differential quadrature method (DQM), employing Chebyshev–Gauss–Lobatto interpolation for high numerical precision. The model's accuracy and robustness are validated through comparison with finite element (FE) simulations and experimental results available in the open literature, under certain simplifying assumptions. This cross-validation confirms the reliability of the proposed approach for predicting transient responses in thermomechanically loaded rotating systems. Parametric investigations reveal the critical influence of gradient index, rotational speed, and thermal gradient on the displacement, velocity, and acceleration fields. The results show that bi-directional material gradation significantly improves the disk's resistance to thermal shocks and mechanical disturbances. These findings contribute valuable insights for the optimized design of high-performance, thermally resilient brake disks in modern automotive applications.