Application of proper orthogonal decomposition to structural vibration analysis

Mode shapes of a structure can be extracted without measuring a series of frequency response functions by implementing proper orthogonal decomposition on the measured response data. If the proper orthogonal decomposition is applied on the time responses of the structure, only one proper orthogonal mode converges to the true normal modes of the structure. The degree of deviation of the other extracted proper orthogonal modes from the true normal modes of the structure depends on the spatial resolution, which is determined by the number of response measurement positions. The suggested procedure of applying the proper orthogonal decomposition to the cross-spectral density functions can extract all of the normal modes contained in the structural responses without suffering from the limitation of the number of response measurement positions. Experimental data of a homogeneous free-free beam and a non-homogeneous free-free beam were used to compare the proper orthogonal modes and the structural normal modes, and the results strongly support the applicability of the proper orthogonal decomposition to the structural vibration analysis. (C) 2003 Elsevier Science Ltd. All rights reserved.