Modal Analysis With Smooth Karhunen-Loe`ve Decomposition

In this paper, the Smooth Orthogonal Decomposition is formulated in term of a Smooth Karhunen-Loe`ve Decomposition (SKLD) to analyze random fields. The SKLD is obtained solving a generalized eigenproblem defined from the covariance matrix of the random field and the covariance matrix of the associated time derivative random field. The main properties of the SKLD are described and compared to the classical Karhunen-Loe`ve decomposition. The SKLD is then applied to the responses of randomly excited vibrating systems with a view to performing modal analysis. The associated SKLD characteristics are interpreted in case of linear vibrating systems subjected to white noise excitation in terms of normal modes. Discrete and continuous mechanical systems are considered in this study.