Analytical models for nonlinear responses of a laboratory solar array

With the advent of large, flexible substructures on-orbit, such as the radiators and solar arrays of the International Space Station (ISS) and the solar arrays of the Hubble Space Telescope (HST), the complexity of the dynamic response of these elements has become a key issue in their performance and in their influence on the system performance. To understand potential issues, an experimental survey was previously conducted of a flexible solar array laboratory model. Superharmonic resonances, subharmonic resonances, combination resonances, jumps, saturation, and modal energy exchange were observed. In this paper, two models are developed to analyze nonlinear planar responses of the solar array. Model I is a base-excited, cantilevered, inextensible beam with a tip mass. Model II is a double-T-shaped structure which includes the flexibility of the array cross bars. Equations of motion are derived. Responses to longitudinal base excitations are compared to experimental behaviors to evaluate appropriateness of the models.