Investigation of nonlinear vibration in spacecraft with flexible solar arrays during penumbra phase

• A nonlinear analytical model is proposed to study vibration phenomena in spacecraft with flexible solar arrays during shadow and penumbra phases. • The model accounts for geometric nonlinearity and its impact on the angular adjustments of solar panels due to varying thermal wave propagation speeds. • The study identifies resonance-like phenomena that can negatively affect satellite performance if not properly managed. • Structural stiffness is found to play a critical role in controlling angular changes and ensuring mission success. • A set of reduced-order nonlinear ordinary differential equations (ODEs) is derived using the Method of Multiple Scales (MMS) to analyze spacecraft dynamics. • Two uncoupling approaches are explored, with at least two internal resonance conditions identified through MMS. • Resonance conditions specific to the Hubble Space Telescope (HST) are examined and validated through time simulations and fast Fourier transform (FFT) analysis. This study presents a nonlinear analytical model for spacecraft equipped with flexible solar arrays, focusing on the nonlinear vibration phenomena induced by the geometric nonlinearity of these arrays during the satellite's shadow and penumbra phases. The performance of the satellite is highly sensitive to changes in the angles of the solar panels relative to their width. Variations in the speed of thermal wave propagation can lead to unintended adjustments in these angles. Changes in the speed ratio of thermal wave propagation relative to the speed of light as a geostationary satellite experiences varying conditions of shadow and penumbra during a solar eclipse. If not properly managed, these changes may result in resonance-like phenomena, negatively impacting the satellite's functionality. Therefore, The angular changes are critically dependent on structural stiffness, which is essential for maintaining data quality and ensuring the scientific success of the satellite's mission.The proposed model incorporates thermoelastic linear coupling terms arising from mass imbalance and thermal forces. The solar arrays are coupled by nonlinear terms, primarily characterized by nonlinear stiffness. The bending-bending-torsion equations of motion include only quadratic nonlinear terms. An explicit set of reduced-order nonlinear ordinary differential equations (ODEs) is derived for the flexible spacecraft using the method of multiple scales (MMS). Two approaches for uncoupling the system are considered, and at least two internal resonance conditions are identified through MMS. As the length of the solar arrays increases, resonance conditions specific to the Hubble Space Telescope (HST) emerge. These predicted resonance conditions are further examined through time-domain simulations and fast Fourier transform (FFT) analyses.