Dynamical Analysis of Large Prestressed Foldable Arrays—Natural Frequency Bounds

The dynamic properties of vibration of large spacecraft structures play an important role in the design of these structures, and yet computing the most basic property, the natural frequency of vibration, is challenging for the scalable deployable structures for the Caltech Space Solar Power Project. These structures consist of bending-stiff trapezoidal frames forming concentric squares, attached to prestressed tapes supported by diagonal deployable booms. A fully connected version of these structures is introduced, from which upper bounds on the natural frequencies can be computed rather easily. These bounds are useful to determine the geometry and material properties for the structural components, before moving to the more complex and time-consuming analysis of the actual, prestressed structures. Results from both sets of analyses are presented for structures ranging in size from 10 to 60 m. In addition, a simplified analytical beam model is developed to estimate the fundamental vibration mode with reasonable accuracy.