Lumped and Distributed Parameter Models of a Spacecraft with Elastic Appendages: Exact Frequencies and Mode Shapes

摘要

Two distinct structural dynamics models for a spacecraft with a symmetric pair of flexible appendages are developed. The first model is a lumped parameter idealization in which the appendages are depicted by rigid bodies attached to the spacecraft central body by torsional springs. In the second model, the appendages are represented by Euler-Bernoulli beams rigidly attached to the spacecraft central body at their roots and free at their terminal end points. Appendages such as long slender antennas and solar arrays can be approximated by both idealizations where for the later case, the primary bending modes of the spacecraft are characterized by deflections of the solar arrays out of their nominal planes. The system natural frequencies and mode shapes are determined analytically, and the effects of geometric offsets are explicitly shown. For the continuum model, the orthogonality conditions for the symmetric and antisymmetric modes are established in the form of an inner product which diagonalizes the system kinetic and potential energies.