A finite-volume transfer matrix formulation for the Eigenanalysis of twisted rotating beams

Accurate dynamic analysis of rotating beams is essential for the design and optimization of rotorcraft components, such as helicopter and tiltrotor blades, which often exhibit high built-in twist and strong elastic-inertial coupling. This study introduces a transfer matrix formulation that integrates the finite-volume beam formulation into the transfer matrix method framework. The approach combines the modularity and compactness of the transfer ma trix method with the modeling fidelity of the finite-volume beam formulation, representing geometrically and inertially coupled beams without requiring the assembly of large global stiffness and inertia matrices. A general ized finite-volume transfer matrix formulation for rotating beams is derived, providing a compact and consistent three-dimensional representation that captures centrifugal stiffening and coupling effects. The method's accuracy is demonstrated through comparison with exact solutions for a uniform cantilever beam over a wide range of rotational velocities. The approach is further assessed for twisted rotating beams, showing good agreement with flexible multibody and finite element analyses. The main effects of rotational velocity, stiffness ratio, and built-in twist on the eigenfrequencies and mode shapes of rotating beams are also investigated. Finally, the formulation is applied to a coupled tiltrotor rotor-drivetrain system, illustrating its capability to capture structural-dynamic coupling effects in more complex assemblies.