Development and application of a nonlinear modal analysis technique for MDOF systems

This work presents a frequency-domain technique that extends the concept of linear modal superposition to nonlinear systems by using the normal nonlin ear mode approach so that a generalized parameter identification method can be formulated for MDOF nonlinear systems. The methodology is compatible wi th existing established vibration analysis techniques such as finite elemen t (FE) modeling and experimental modal analysis. Furthermore, once the nonl inear modal parameters are identified at some reference force level, the no nlinear response can be predicted at any arbitrary excitation level using s tandard modal summation techniques. The numerical study is focused on a 4-D OF system with friction damping nonlinearity, for which both the macro- and microslip representations are considered. Simulated nonlinear frequency re sponse functions, obtained for a given excitation level using a harmonic ba lance method, were subjected to a nonlinear modal analysis procedure, and t he modal parameters were extracted as a function of the vibration amplitude . Micro- and macroslip representations yielded significantly different nonl inear modal parameters, though the findings were consistent with those of o ther researchers. The nonlinear modal analysis results and the response pre dictions at arbitrary forcing levels were compared against reference harmon ic balance simulations, and very good agreement was observed for all cases investigated. it was verified that the friction damper produced highest dam ping for the vibration amplitude of maximum energy dissipation.