Frequency Based Nonlinear Decoupling Using Experimentally Measured Quasi-Linear FRFs.

Decoupling methods based on measured Frequency Response Functions (FRFs) are well established for linear systems, yet their extension to nonlinear systems remains in its infancy. Existing frequency-based decoupling techniques for nonlinear systems are limited to localized nonlinearities and specific configurations that require prior knowledge of the nonlinearity location; a general decoupling method for nonlinear systems does not yet exist. This paper introduces a general nonlinear decoupling framework. The proposed Nonlinear Frequency-Based Decoupling (NL-FBD) framework uses quasi-linear FRFs of the coupled system via response-controlled testing (RCT), and measured or calculated FRFs of the known substructure; and then applies a linear decoupling formulation, to calculate the quasi-linear FRFs of the unknown nonlinear structure at several response levels. Subsequent linear modal identification yields response-dependent nonlinear modal parameters, which are then used to synthesize constant-force FRFs of the unknown nonlinear substructure. The proposed approach is capable of; i) handling multiple nonlinear elements located arbitrarily within the structure, ii) addressing systems even with distributed nonlinearities, iii) accommodating nonlinearities in both substructures, and iv) achieving decoupling at multiple degrees of freedom. The applicability limits of the proposed approach are examined in detail, together with an assessment of its accuracy through numerical case studies. In particular, nonlinearities in both substructures are demonstrated for the single degree-of-freedom connection case, whereas multiple-degree-of-freedom connections are investigated for systems with a known linear substructure. Experimental validation on a nonlinear beam--linear beam assembly confirms that NL-FBD accurately decouples the unknown nonlinear beam, yields a reliable nonlinear modal model, and predicts the forced response of a new assembly incorporating the decoupled nonlinear beam, with excellent agreement to measurements even at high forcing levels.