Model reduction of semi-positive definite systems reflected to actuator and sensor locations

A model reduction method for large flexible structures is developed in orde r to deal with rigid-body modes and to obtain higher modes related to start ing vectors corresponding to multi-directional locations of actuators and s ensors. The algorithm is involved with the frequency shifting technique, Kr ylov vector sequence and the inverse iteration method. The reduced-order mo del by the proposed algorithm has shown better dynamic response than the mo del constructed by truncated eigenvectors of a full-order system because th e eigenvectors are not always the best choice in a dynamic analysis. Futher more, the algorithm for a semi-positive definite system can accommodate a d amping effect so that the efficient vectors depending on load vectors can b e produced without increasing the system order and without using complex ca lculus, unlike the standard eigenproblem with damping effect. Numerical exa mple is given with a flexible space structure characterized by closely spac ed eigenvalues.