Karhunen-Loève modes of a truss: Transient response reconstruction and experimental verification

Karhunen-Loève (K-L) or proper orthogonal decomposition modes are used to discretize the dynamics of a four-bay linear truss. This is achieved by defining global K-L modal amplitudes and employing the orthogonality relations between K-L modes that are inherent in the K-L decomposition. It is found that the K-L-based low-order models can capture satisfactory the transient dynamics of the truss, even when only a limited number of them is used for the order reduction. A comparison between the exact and low-order dynamics in the frequency domain reveals that the low-order models capture the leading resonances of the truss. A series of experiments with a practical three-bay truss is then performed to validate the theoretical K-L decomposition. A comparison between theory and experiment indicates agreement between the predicted and realized dominant K-L mode shapes, but less so in the higher-order modes. The reasons for this discrepancy between theory and experiment are discussed, and possible applications of the K-L-based order reduction to passive and active control of practical large-scale flexible systems are outlined.