Nonlinear modal interactions in a beam-mass system tuned to 3:1 and combination internal resonances based on correspondence between MTS and NSI methods

•Nonlinear modal interactions in large amplitude vibrations of beam-mass system.•Internal resonances caused by addition of a mass-spring-damper to a beam.•Stability, bifurcations, and energy exchanges based on multiple time scales method.•A correspondence between multiple time scales and nonlinear system identification in modal interactions.•Variations of IMF amplitudes used to understand energy exchange among associated modes. In this article, a correspondence between multiple time scales (MTS) results and nonlinear system identification (NSI) method is established to identify nonlinear modal interactions in large amplitude vibrations of a coupled dynamical system. The system is a beam carrying a mass-spring-damper (MSD) system tuned to 3:1 and combination internal resonances caused by MSD parameters. The energy exchange mechanisms and modal interactions among the first three vibration modes are interpreted based on the modal amplitudes extracted by the MTS method. However, these amplitudes are not available in practical measured time series. Therefore, to detect the modal interactions based on measured data, time-frequency analysis beside NSI is employed. To this end, the mono-frequency components of the time series are studied by extracting intrinsic mode functions (IMFs), and a correspondence between the IMFs amplitudes and MTS results is determined to comprehend the energy exchanges in the system. Accordingly, by applying NSI for different values of excitation frequency, energy exchange among the modes is understood without the necessity of modal amplitudes. Moreover, the dominant dynamic behavior of the time response, i.e. periodic, quasi-periodic, and chaotic behaviors are determined, and beating-like phenomenon in the IMFs is investigated.