An extension of force appropriation to the identification of non-linear multi-degree of freedom systems

Classical force appropriation methods are used in the identification of lin ear systems to determine the multi-point force vector that will induce sing le-mode behaviour, thus allowing each normal mode to be identified in isola tion. This paper presents an extension to this linear approach that will en able the approximate identification of multi-degree-of-freedom (d.o.f.) sys tems with weak non-linearity on a similar basis. The classical linear modal model is used, with additional terms included to represent the direct non- linear restoring forces of the system. Using this force appropriation for n on-linear systems (FANS) method, a force vector with harmonics present is d erived using an optimization approach such that the response of the system is restricted to that of a target mode, but in the non-linear region. The r esponse obtained from several force levels is then curve fitted using the r estoring force method applied in linear modal space so as to yield the dire ct linear and non-linear modal parameters for the target mode. The method i s applied to a simulated two-d.o.f. example and good agreement is found bet ween estimated and true parameters. An extension to the identification of c ritical non-linear modal cross-coupling terms is proposed. (C) 2000 Academi c Press.