Abstract
The Karhunen-Loe`ve (KL) theory establishes that a second-order random field can be expanded as a series involving a sequence of deterministic orthogonal functions with orthogonal random coefficients. The KL theory can be applied to the responses of randomly excited vibrating systems with a view to performing a decomposition in separate variable (time and space) form giving a modal analysis tool. An averaging operator involving time and ensemble averages is used to draw up the KL theory. This averaging operator can be applied in stationary cases as well as non-stationary (transient) ones. The purpose of this paper is to compare the KL modes obtained from the displacement field, velocity field, and displacement-velocity field. Stationary as well as transient (non stationary) cases will be considered. The physical interpretation of the KL modes will be also investigated.
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