Efficient buckling and free vibration analysis of cyclically repeated space truss structures

Eigenproblems play a key role in the stability and free vibration analysis of structures. In large structural models, the solutions of these problems need a considerable computational effort. There are special types of structures whose special properties can be utilized to achieve solutions in a much simpler way. In this paper, an efficient method is presented for buckling and free vibration analysis of cyclically repeated space truss type structures. First, for a three dimensional truss element, stiffness, geometric stiffness and mass matrices are expressed in cylindrical coordinate system and this leads to the formation of a special pattern for the related matrices of entire of such structures. Second, using this pattern where some concepts of Kronecker product, initial generalized eigenproblems are decomposed into some subproblems with smaller dimensions and their solutions can easily be obtained. Finally, the efficiency of the present method is illustrated through some examples.