Higher-order nonlinear modeling and multi-modal performance of axially restrained diverse flexible shaft-disk assemblies

Flexible shaft-disk combinations are essential in engines, turbines, and machinery. Understanding their modal characteristics is vital for industry-wide performance, reliability, and safety. This study uses higher-order modeling and multi-modal analysis to grasp complex dynamics, especially with multiple disks of varied sizes. Employing Hamilton’s method and Galerkin’s technique, equations of motion are formulated and then utilized for multi-modal analysis considering structural nonlinearity. Various shaft-disk arrangements are analyzed, including disk number, size, position, and shaft material, to understand their impact on modal behavior. The findings reveal the substantial impact of disk count, sizes, and placements on modal dynamics and intricate vibration characteristics across diverse spinning speeds. This effect is accentuated by integrating higher-order modeling into multi-modal analysis. Notably, higher-order deformation enhances overall resilience capacity and imposes more effective vibration restrictions than the linear approach. Furthermore, the investigation explores how different shaft materials influence modal characteristics, critical speeds, and vibration amplitudes in various shaft-disk combinations. Theoretical findings are validated using numerical results from 3D finite element-based models simulated with ANSYS 3D for accuracy. Ultimately, the study introduces a theoretical framework adaptable to numerous flexible shaft-disk combinations, offering a valuable resource for understanding and enhancing system behavior, benefiting engineers and researchers alike.