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

• Published in: Journal of sound and vibration 1998-06, Vol.213 (4), p.673-708
• Main Authors: Richards, C.M., Singh, R.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Measurement and testing methods; Measurement methods and techniques in continuum mechanics of solids; Physics; Solid mechanics; Structural and continuum mechanics
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.1998.1522

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.