Nonlinear Vibrations of Cyclically Symmetric Structures: Basic Properties and a Method for Calculation

A method for analysis of essentially nonlinear vibrations of cyclically symmetric structure has been developed. Two major cases are analysed: (i) steady-state periodic multiharmonic vibrations; (ii) transient vibrations. The method allows exact calculation of the essentially nonlinear vibrations to be performed using a model for only one period of the cyclic symmetry. A rigorously proof of possibility of such calculations is given. Special conditions for excitation forces and initial conditions defining when the cyclic symmetry properties can be efficiently applied in the dynamic analysis are derived and basic properties of the nonlinear vibrations of the cyclically symmetric structures are analysed. For analysis of periodic vibrations the multiharmonic balance formulation for the cyclically symmetric structures is developed. Numerical investigations demonstrate capabilities of the method for analysis of forced response of cyclically symmetric structures with different types of nonlinear interaction. Properties of the forced response and vibration modes of these structures are examined.