Identification of multi-degree-of-freedom non-linear systems under random excitations by the "reverse path" spectral method

Conventional frequency response estimation methods such as the "H-1" and "H-2" 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 "H-c1" and "H-c2" 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 ar: 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. (C) 1998 Academic Press Limited.