Experimental Verification of a Recently Developed FRF Decoupling Method for Nonlinear Systems

Abstract

The FRF Decoupling Method for Nonlinear Systems (FDM-NS), recently proposed by the authors of this paper, is a technique based on predicting the dynamic behavior of a particular substructure of a coupled nonlinear structure from the knowledge of the measured FRFs of the coupled nonlinear structure and calculated or measured FRFs of the other substructure. The uncoupled substructure can be linear or nonlinear. The method is applicable to systems where the nonlinearity can be represented as a single nonlinear element. The method has been experimentally verified for a structure having a grounded nonlinear element. In this work, the applicability of the method to a structure having an internal nonlinearity is demonstrated. The test system used in this study is composed of two cantilever beams where their free ends are connected to each other with two identical thin beams which introduce an internal nonlinearity to the coupled structure. In this test, the FRFs of the coupled nonlinear assembly are measured in a frequency range for various different constant displacement levels of the nonlinear connection element. Tip point transverse FRFs of one of the cantilever beam, which is taken as the known subsystem, are also measured. By using the decoupling method proposed the modal parameters of the unknown nonlinear subsystem are calculated as a function of the relative displacement amplitude between ends of the nonlinear connection element, from which the dynamic response of the decoupled subsystem can be calculated for any harmonic excitation. In order to demonstrate the accuracy of the method, the decoupled system is connected to a cantilever beam with a different length, and firstly, the FRFs of the coupled new system are calculated for constant amplitude harmonic forcing. Then, the calculated FRF curves are compared with those which are directly measured.