Accuracy of Nonlinear Substructuring Technique in the Modal Domain

The dynamic analysis of complex engineering systems can be performed by considering the assemblies as composed of subsystems and coupling them through substructuring techniques. A technique in the modal domain called Nonlinear Coupling Procedure (NLCP) has been recently defined to couple subsystems connected through nonlinear connections by using their Nonlinear Normal Modes (NNMs). It manages to capture the main dynamic features of the system, i.e., the backbone of each NNM, and it provides satisfactory results in terms of mode shape and resonance frequency as function of the excitation level of the assembled system, with a considerable reduction of the computational time. However the results may be inaccurate due to approximations either in the models of the subsystems or due to the considered coupling technique. Furthermore, nonlinear subsystems can be the cause of complex behaviors of the assembly and then their models need to be carefully characterized. Thus, it is necessary to evaluate the reliability of the method in terms of the accuracy of the solution. This is done by defining a reliability ratio based on energy concepts depending on the level of the excitation acting on the system. The effectiveness of the reliability ratio of nonlinear techniques is verified on the NLCP applied to a mechanical system with localized nonlinearities.