Vibration model of coilable mast considering slack diagonals

After the coilable mast deploying, the battens are curved and the diagonals are tensioned because of the preload. The diagonals can be slack for large amplitude vibration. A vibration model was constructed to describe the fundamental frequency characteristic of that status. The curved batten and slack of diagonals was considered. The batten with small stiffness in curved status and preload was simulated with a rod with small elastic modulus and corresponding strain, and one rod element was modeled to simulate two cables which slacked in different time. The coilable mast before and after diagonals slack was treated as two different structures, and their finite element method (FEM) models were constructed with Ansys. Two fundamental frequencies were computed. Then the coilable mast was equivalent to a continuous beam with pricewise linear stiffness, the pricewise stiffness correspond to the different structure before and after the diagonals slack. Considering the criterion of diagonals slack obtained with that FEM model, the vibration equation of coilable mast with large amplitude was established. Using equivalent linearization method, the relationship between equivalent frequency of coilable mast and the top-end amplitude can be obtained. The result can be verified with transient analysis of Ansys. The model and result is helpful for the design and vibration control of coilable mast.