The rise of Electric Vertical Take-Off and Landing (E-VTOL) vehicles, driven by the demand for fast urban transport, emphasizes the need to understand and mitigate aeroelastic instabilities like whirl-flutter, particularly in designs with distributed electric propulsion systems. Historically, whirl-flutter has caused catastrophic failures, highlighting the need for comprehensive analysis in modern aircraft designs. This work aims to develop a comprehensive computational model using the Finite Element Method to fully capture the dynamics between rotating, expressed in a floating frame of reference, and stationary parts of a structure, enabling a more accurate study of the whirl-flutter phenomenon. This analysis uses the Floquet theory to study the system's stability, particularly in a fixed-rotating frame of reference. The model includes an innovative time-dependent mechanical coupling strategy for the mass, gyroscopic, and centrifugal stiffness structural matrices, therefore fully preserving the dynamics of the structure. The methodology involves the validation of various finite element matrices and components derived from 3D beam elements, followed by the implementation of time-dependent coupling between rotating and stationary components. The developed model is applied to a wing-propeller structure, illustrating its capability to work on complex geometry structures. The results show that the partial coupling between translational degrees of freedom of rotating structures and those of the stationary structure at the hub, is successfully validated. However, it is demonstrated that the Newmark integration scheme does not provide consistent results, highlighting the need for alternative approaches for accurate time integration. This partial success demonstrates the potential of the developed model as a tool for accurately capturing critical dynamics in whirl-flutter analysis, contributing to the design and certification of future urban air mobility vehicles.