Application of Auto-Covariance Orthogonal Decomposition in the Response of Multi Degree of Freedom (MDOF) Systems to Non-Stationary Random Vibration Processes

Abstract

The Karhunen-Loeve expansion method has been utilized in the decomposition of random forcing auto-covariance functions. A recent study by the authors provided proof that such a decomposition could be used to nd the response of a SDOF system to non-stationary loading. In this study, the authors are modifying the method to be further generalized and applicable to multi degree of freedom systems. As a rst step the existing method is modi ed by switching from continuous to piecewise constant basis functions. Such a change allows the method to be applied to any covariance function and can demonstrate superior e ciency over continuous functions where the eigenvectors of the covariance function are not well known. The modi cations implemented have been applied to a single degree of freedom system studied previously by the authors and also simple 2DOF systems to keep the derivation process clear. Response due to non-correlated forcing caused by a variety of covariance functions are presented and validated with an analytical solution.