Nonlinear softening effects in rigid-flexible coupled spacecraft

A nonlinear dynamic model of a rigid-flexible coupled spacecraft consisting of a central rigid hub and two flexible solar panels with tip masses is established to investigate inertial coupling mechanisms in large flexible spacecraft. An analytical framework based on the method of multiple scales is developed by reformulating the perturbation solution for coupled rigid-flexible systems. Steady-state responses and stability conditions under both non-resonant and primary resonant conditions are derived and verified by direct numerical simulations. The results show that rigid-flexible inertial coupling leads to an overall stiffness-softening behavior, resulting in resonance frequency shifts, multivalued responses, jump phenomena, and hysteresis. By separating different nonlinear inertial terms, it is found that tangential and nominal inertial forces mainly contribute to the softening behavior, whereas Coriolis coupling introduces a hardening effect. Parametric studies indicate that the flexible panel length affects the nonlinear response through coupled variations in natural frequency, damping, and inertial coupling strength, while increasing the hub rotational inertia weakens the softening characteristics. Although axial centrifugal force increases the resonance frequency and alleviates the softening effect, the system still exhibits dominant softening nonlinearity. These results provide guidance for the dynamic design and vibration control of large flexible spacecraft.