Nonlinear vibration of beam structures: Analytical and explicit dynamics FEA evaluations

Orbiting platforms of the size and complexity of the impending International Space Station (ISS) present many challenges. Among these is anticipating and understanding the dynamics of the large, flexible, deployable solar arrays. An experimental survey with a laboratory model solar array (support structure only) revealed nonlinear behaviors including subharmonic and combination resonance, jumps, and modal energy exchanges. A smaller benchtop model array exhibited similar phenomena. With longitudinal base excitation of the arrays representing vibrational motion of the spacecraft, repeated failures of the lower crossbars of the models occurred. This was unexpected due to the small-amplitude motion of the mast at the lower crossbar attachment point. In this dissertation, non-linear models are developed to show that the failures can be attributed to a combination resonance of the 3rd (mast) and 5th (lower crossbar) modes.; The explicit dynamics finite element analysis approach has been used successfully for the prediction of short-time, large-deformation transient response. In this paper, this approach is applied for the prediction of steady-state, large-deformation transient response—in particular, for the transverse response of a thin cantilevered beam subjected to axial parametric base excitation of the first mode. Results were compared to experimental results available in the literature. The frequency response predicted by the explicit dynamics approach is remarkably consistent with the experimental frequency response. Guidelines are suggested for the applied load time step and modal damping, which were noted as critical variables. Current limitations are identified in the commercial software that needs to be circumvented to allow application for nonlinear structural response over a broader frequency range.