Thermo-flexible coupled modeling and active control of thermally induced vibrations for a flexible plate

Flexible spacecraft exhibit thermal-structural coupled effects in space thermal environment, leading to issues such as thermally induced deformations and vibrations. It is crucial to accurately predict the thermally induced dynamic behaviors of space structures and to actively control them. Accordingly, an integrated computational framework is constructed to work out the multi-physics coupled problem by synchronously solving the displacement and temperature fields. Firstly, the coupled thermoelasticity of the model is characterized by the thermo-flexible fully parameterized absolute nodal coordinate formulation (ANCF), wherein temperature gradients, utilized as nodal coordinates, are directly employed to calculate the temperature difference between arbitrary points. The viscoelastic constitutive relationship of the material is considered based on the Kelvin-Voigt model. Secondly, a comprehensive thermal analysis of the complicated space environment is conducted, and the transient heat conduction equation incorporating thermal radiation is derived via the weighted residual method. Furthermore, several numerical examples are analyzed, and corresponding finite element models are established to validate the effectiveness and accuracy of the developed coupling method. Subsequently, the temperature gradient feedback (TGF) control law is established by employing thermal actuators mounted on the structure's surface. Controlling thermal bending moments, generated by the temperature gradients resulting from the heat fluxes of the heaters, are used for active vibration suppression. Finally, the effects of different parameters on thermally induced vibrations in a cantilevered plate and corresponding active control strategies are examined. The findings in this work provide theoretical foundations and practical significance for predicting and actively controlling thermally induced responses in large flexible space structures.