Smooth Orthogonal Decomposition for Modal Analysis of Randomly Excited Systems ⋆

Modal parameter estimation in terms of natural frequencies and mode shapes is studied using smooth orthogonal decomposition for randomly excited vibration systems. This work shows that under certain conditions, the smooth orthogonal decomposition eigenvalue problem formulated from white noise induced response data can be tied to the unforced structural eigenvalue problem, and thus can be used for modal parameter estimation. Using output response ensembles only, the generalized eigenvalue problem is formed to estimate eigen frequencies and modal vectors for an eight-degree-of-freedom lightly damped vibratory system. The estimated frequencies are compared against system frequencies obtained from structural eigenvalue problem and estimated modal vectors are checked using the modal assurance criterion. Simulations show that for light damping, satisfactory results are obtained for estimating both system frequencies and modal vectors.