ON THE CHOICE OF APPROPRIATE BASES FOR NONLINEAR DYNAMIC MODAL-ANALYSIS

This paper focuses on assessing the accuracy of various modal bases in nonlinear dynamic modal analysis of helicopter rotor blades by comparing their prediction with a reference solution obtained by integrating in time the full finite element equations. Both the full finite element and the modal models are based on the same discretization of the physical problem, and are derived from a mixed variational principle. This variational statement is a purely algebraic, fourth order expression that is ideally suited for modal reduction. Perturbation modes, which extract information about the nonlinear behavior of the structure from higher order derivatives of the variational principle, are shown to provide an excellent basis for the modal analysis, as they accurately capture the nonlinear kinematic couplings. Perturbation modes provide a more accurate model than that based on natural vibration mode shapes, which are very poor at synthesizing these nonlinear kinematic couplings. However, in the presence of nonlinearities associated with rotational dynamic effects, both natural vibration and perturbation mode shapes fail to accurately represent the dynamic behavior of the blade.