Multi-harmonic equivalent modeling for a planar repetitive structure with polynomial-nonlinear joints.

How nonlinear joints affect the response of large space structures is an important problem to investigate. In this paper, a multi-harmonic equivalent modeling method is presented to establish a frequency-domain model of planar repetitive structures with nonlinear joints. First, at the local level, the nonlinear joint is modeled by the multi-harmonic describing function matrix. The element of the hybrid beam is obtained by the dynamic condensation of the beam-joint element. Second, at the global level, the displacement-equivalence method is used to model the multi-harmonic Euler continuum beam equivalent to the planar repetitive structure. Then, the pseudo-arc-length continuation method is applied to track the multi-harmonic trajectory of response. Afterwards, an experiment is conducted to validate the correctness of the modeling method, considering the effect of hanging rope and air damping. In the numerical studies, several simulation results indicate the similarity of response between a single-degree-of-freedom system with a single nonlinear joint and the system of the planar repetitive structure with a large number of nonlinear joints. Finally, the component of higher-order harmonics is shown to be important for predicting the resonance frequencies and amplitudes. [ABSTRACT FROM AUTHOR]