A Novel Transfer Matrix Formulation for Rotating Beams

The dynamic analysis of rotating beams is fundamental for the design and optimization of rotorcraft components, such as helicopter and tiltrotor blades. These structures exhibit high twist rates, geometric nonlinearities, and complex elastic and inertial coupling effects, making their modeling particularly challenging. This study presents a novel transfer matrix formulation for the analysis of rotating beams, developed by integrating the Finite Volume Beam formulation into the Transfer Matrix Method. The proposed model is fully three-dimensional and accounts for elastic and inertial coupling and centrifugal stiffening effect, ensuring an accurate representation of structural dynamics in rotorcraft applications. The resulting recursive formulation provides an efficient and effective alternative to global finite element methods to model rotating structures. The proposed method is validated against benchmark cases and a representative rotor blade. Comparisons with high-fidelity model demonstrate excellent agreement while highlighting the computational advantages of the transfer matrix approach. The results illustrate the critical influence of rotational speeds on natural frequencies and mode shapes. This study provides a powerful tool for analyzing rotating beams. The proposed formulation offers a computationally efficient and reliable tool for preliminary design and optimization, facilitating the study of complex structural dynamics in rotorcraft systems.