<p>This study delves into the nonlinear dynamics of hollow tapered multi-disk shaft systems using the fundamental mode Galerkin method applied to a large deflection model. This analysis incorporates factors such as rotary inertia, gyroscopic effects, and axial constraints, all of which significantly influence the system’s vibration response. Closed-form analytical solutions for both linear and nonlinear natural frequencies are derived using the method of multiple scales, with validation provided through ANSYS simulations. The study further investigates the system’s modal characteristics and its response to mass imbalance excitations through various tools, including time histories, Fast Fourier Transforms, Campbell diagrams, Poincaré maps, amplitude-frequency response curves, and amplitude variations with eccentricity and damping. The findings show that nonlinear natural frequencies consistently exceed the linear ones, with their variations influenced by factors such as taper ratio and internal diameter. Increasing the taper ratio reduces the beating periods, raises nonlinear frequencies, and lowers amplitude contributions up to a certain threshold, after which these contributions increase. In contrast, a larger internal diameter improves system stability and accelerates the settling time. The system predominantly exhibits hardening behaviour, with multiple jump phenomena and solutions emerging under slight parametric shifts in both primary and superharmonic resonance conditions. The results suggest that carefully choosing design variables can shift the system from a bistable vibration state to a monostable solution, promoting a smooth, jump-free steady-state response and reducing the risk of instability and failure. This study emphasizes the importance of accurate system modelling in high-speed applications, where even small mass imbalances can significantly impact performance and stability, highlighting the need for thoughtful design adjustments to ensure reliability.</p>