Nonlinear normal modes and their application in structural dynamics

Abstract

Recent progress in the area of nonlinear modal analysis forstructural systems is reported. Systematic methods are developedfor generating minimally sized reduced-order models thataccurately describe the vibrations of large-scale nonlinearengineering structures. The general approach makes use ofnonlinear normal modes that are defined in terms of invariantmanifolds in the phase space of the system model. An efficientGalerkin projection method is developed, which allows for theconstruction of nonlinear modes that are accurate out to largeamplitudes of vibration. This approach is successfully extended tothe generation of nonlinear modes for systems that are internallyresonant and for systems subject to external excitation. Theeffectiveness of the Galerkin-based construction of the nonlinearnormal modes is also demonstrated for a realistic model of arotating beam.