Dynamic behaviors of rigid shaft-flexible SMPSA coupling system

Shape-memory polymer solar array (SMPSA) are promising for space applications due to their large deformability and self-deployment capability. An integral-form stress-stain constitutive relationship is proposed for the shape-memory polymer (SMP) based on the three-element model to permit the dynamic modeling of the SMPSA, the validity of which is verified by the reproduction of the shape-memory effects of the SMPSA in the numerical simulation. With the proposed constitutive relationship, the dynamic equations of the hub-beam model describing the coupling dynamic problem of the rigid shaft-flexible SMPSA coupling system are derived based on the Hamiltonian principle. Then, the generalized multi-symplectic formulations for the vibration equation of the SMPSA are deduced and the symplectic Runge-Kutta method is employed to discrete the decomposed form of which. From the numerical results, it can be found that, different from the non-dissipative vibration of the traditional solar array, the vibration of the SMPSA will dissipate spontaneously. The effects of the external torque with variable amplitude or frequency and the ambient temperature on the dynamic response of the SMPSA are also explored in detail. The findings reported in this paper give some guidance for the control design of the rigid shaft-SMPSA system in the unfolding process.