Development and Application of a Nonlinear Modal Analysis Technique for MDOF Systems

摘要

This work presents a frequency-domain technique that extends the concept of linear modal super-position to nonlinear systems by using the normal nonlinear node approach so that a generalized parameter identification method can be formulated for MDOF nonlinear systems. The methodology is compatible with existing established vibration analysis techniques such as finite element (FE) modeling and experimental modal analysis. Furthermore, once the nonlinear modal parameters are identified at some reference force level, the nonlinear response can be predicted at any arbitrary excitation level using standard modal summation techniques. The numerical study is focused on a 4-DOF system with friction damping nonlinearity, for which both the macro- and microslip representations are considered. Simulated nonlinear frequency response functions, obtained for a given excitation level using a harmonic balance method, were subjected to a nonlinear modal analysis procedure, and the modal parameters were extracted as a function of the vibration amplitude. Micro- and macroslip representations yielded significantly different nonlinear modal parameters, though the findings were consistent with those of other researchers. The nonlinear modal analysis results and the response predictions at arbitrary forcing levels were compared against reference harmonic balance simulations, and very good agreement was observed for all cases investigated. It was verified that the friction damper produced highest damping for the vibration amplitude of maximum energy dissipation.