<p>This study presents a novel approach to model the nonlinear modal dynamics of multi-disk shafts with dual-mode coupling under axial constraints and large transverse deflections. The present work addresses key aspects of rotor dynamics, including geometric nonlinearity, mode coupling, rotary inertia, and gyroscopic effects. Closed-form expressions for both linear and nonlinear natural frequencies are derived using the method of multiple scales and are validated against numerical simulations. A detailed analysis of modal behavior is conducted through time histories, frequency spectra, Campbell diagrams, and Poincaré maps. The results reveal significant deviations from conventional linear predictions, with nonlinear effects and dual-mode coupling becoming increasingly dominant as elastic deflection amplitudes grow, particularly in lightweight, high-speed, axially constrained multi-disk rotating systems. The inclusion of additional disks gives rise to increasingly complex vibration patterns, including flower-like deformations, spiral trajectories, and multi-lobed mode shapes. In contrast to the relatively simple nonlinear responses observed in single-disk systems, multi-disk configurations exhibit rich, coupled, and highly intricate dynamic behavior. These findings underscore the limitations of linear modeling approaches and highlight the critical importance of incorporating nonlinear effects and mode coupling in the analysis to reliably predict the performance of rotating machinery.</p>