The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balancing technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. The practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweep excitations of increasing amplitudes.Comment: Journal pape

Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the structure and comparisons suggest that the model captures the stiffness and damping accurately over a range of forcing levels.

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or linear time-periodic (LTP). Examples include anisotropic rotor-bearing systems, wind turbines, and nonlinear systems linearized about a periodic trajectory. Many of these have been treated analytically in the literature, yet few methods exist for experimentally characterizing LTP systems. This paper presents a set of tools that can be used to identify a parametric model of a LTP system, using a frequency-domain approach and employing existing algorithms to perform parameter identification. One of the approaches is based on lifting the response to obtain an equivalent linear time-invariant (LTI) form and the other based is on Fourier series expansion. The development focuses on the preprocessing steps needed to apply LTI identification to the measurements, the postprocessing needed to reconstruct the LTP model from the identification results, and the interpretation of the measurements. This elucidates the similarities between LTP and LTI identification, allowing the experimentalist to transfer insight between the two. The approach determines the model order of the system and the postprocessing reveals the shapes of the time-periodic functions comprising the LTP model. Further postprocessing is also presented, which allows one to generate the state transition and time-varying state matrices of the system from the output of the LTI identification routine, so long as the measurement set is adequate. The experimental techniques are demonstrated on simulated measurements from a Jeffcott rotor mounted on an anisotropic flexible shaft supported by anisotropic bearings.