Modal properties of cyclically symmetric systems with central components vibrating as three-dimensional rigid bodies

This study investigates the vibration mode structure of general cyclically symmetric systems with central components vibrating as three-dimensional rigid bodies. This work does not rely on the assumptions of the system matrix symmetries; asymmetric inertia matrix, damping, gyroscopic, and circulatory terms can be present. In the equation of motion of a general cyclically symmetric system, the matrix operators are proved to have properties related to the cyclic symmetry. These symmetry-related properties are used to prove the modal properties of general cyclically symmetric systems. Only three types of modes can exist: substructure modes, translational-tilting modes, and rotational-axial modes. Each mode type is characterized by specific central component modal deflections and substructure phase relations. Instead of solving the full eigenvalue problem, all vibration modes and natural frequencies can be obtained by solving smaller eigenvalue problems associated with each type. This computational advantage is dramatic for systems with many substructures or many degrees of freedom per substructure.