IDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NONLINEAR-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 m ake it difficult to extract underlying linear system properties. To ov ercome 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 singl e-degree-of-freedom non-linear systems. Certain modifications are made in this article for a multi-degree-of-freedom ''reverse path'' formul ation that utilizes multiple-input/multiple-output data from non-linea r systems when excited by Gaussian random excitations. Conditioned ''H -c1'' and ''H-c2'' frequency response estimates now yield the underlyi ng linear properties without contaminating effects from the non-linear ities. Once the conditioned frequency response functions have been est imated, the non-linearities, which are described by analytical functio ns, are also identified by estimating the coefficients of these functi ons. Identification of the local or distributed non-linearities which exist ar: or away from the excitation locations is possible. The new s pectral approach is successfully tested on several example systems whi ch include a three-degree-of-freedom system with an asymmetric non-lin earity, a three-degree-of-freedom system with distributed non-linearit ies and a five-degree-of-freedom system with multiple non-linearities and multiple excitations. (C) 1998 Academic Press Limited.