IDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NON-LINEAR SYSTEMS UNDER RANDOM EXCITATIONS BY THE “REVERSE PATH” SPECTRAL METHOD

Abstract

Conventional frequency response estimation methods such as the “H1” and “H2” methods often yield measured frequency response functions which are contaminated by the presence of non-linearities and hence make it difficult to extract underlying linear system properties. To overcome this deficiency, a new spectral approach for identifying multi-degree-of-freedom non-linear systems is introduced which is based on a “reverse path” formulation as available in the literature for single-degree-of-freedom non-linear systems. Certain modifications are made in this article for a multi-degree-of-freedom “reverse path” formulation that utilizes multiple-input/multiple-output data from non-linear systems when excited by Gaussian random excitations. Conditioned “Hc1” and “Hc2” frequency response estimates now yield the underlying linear properties without contaminating effects from the non-linearities. Once the conditioned frequency response functions have been estimated, the non-linearities, which are described by analytical functions, are also identified by estimating the coefficients of these functions. Identification of the local or distributed non-linearities which exist at or away from the excitation locations is possible. The new spectral approach is successfully tested on several example systems which include a three-degree-of-freedom system with an asymmetric non-linearity, a three-degree-of-freedom system with distributed non-linearities and a five-degree-of-freedom system with multiple non-linearities and multiple excitations.