Graph‐Theory Approach to Eigenvalue Problem of Large Space Structures

The dynamic analysis and control system design of large space structures involve the solution of the large‐dimensional generalized matrix eigenvalue problem. The computational effort involved is proportional to the third power of the dimension of the matrices involved. To minimize the computational time a graph‐theory approach to reduce a matrix to lower‐ordered submatrices is proposed. The matrix‐reduction algorithm uses the Boolean matrices corresponding to the original numerical matrices and, thus, the computational effort to reduce the original matrix is nominal. The computational savings directly depend upon the number of submatrices into which the original matrix is reduced. A free‐free square plate is considered as an example to illustrate the technique. In this example a matrix of 16th order is reduced to three scalars corresponding to three rigid‐body modes, and three matrices of order three and one matrix of order four.