In the automatic transmission (AT) systems of heavy-duty vehicles, the compound planetary gear set (CPGS) is often combined with clutches or brakes to enable multi-speed AT configurations. This requires the center member of the CPGS to connect with the inner hub of the clutch or brake, where engagement of the friction and steel plates allows for power transmission or breaking of the CPGS components. However, vibrations from the CPGS can transfer to the clutch, causing repeated impacts on the inner hub, which may lead to the eventual fracture of the friction plate. This paper investigates the fracture mechanism of the friction plate under CPGS excitation. The CPGS under study comprises one sun gear, two ring gears, one carrier, and multiple short and long planet gears, with the failing friction plate linked to one of the ring gears via spline teeth. This ring gear is designed to float and remains unloaded. To address the impact of these vibrations, we propose a hybrid modeling approach that combines the lumped parameter method and the substructure condensation method. Using this model, we first analyze the dynamic response of the CPGS, focusing on the dynamic impact forces acting on the friction plate due to CPGS excitation and the resulting stress response. Building on these findings, we develop a life-prediction model for the friction plate and assess fracture positions to clarify the fracture mechanism of the friction plate under CPGS excitation.