Nonlinear Normal Mode Estimation with Near-Resonant Steady State Inputs

Abstract

Nonlinear normal modes (NNMs) have been widely used for understanding and characterizing the motion of nonlinear structures, yet current methods to measure them experimentally are time-consuming and not always reliable. Since the structural nonlinearities usually occur when the sample oscillates at high amplitudes, specimens can be damaged or at least develop fatigue cracks when the testing is lengthy. Moreover, the interaction between the shaker and the structure can lead to distortions of the excitation force and can impact the quality of the measured test data. In our previous work, we proposed an NNM estimation algorithm that can help to overcome the issues mentioned above. The approach uses near-resonant data together with an algorithm based on the Single Nonlinear Resonant Mode (SNRM) method to then estimate the NNM backbone. The SNRM algorithm, in its original form, requires vibration modes to be well-separated and assumes no internal resonances between them. This work proposes a possible modification to the algorithm that will allow the modal coupling to be detected as well. The final version of the algorithm will be first tested with data generated numerically using a reduced model of a curved beam experiencing modal interactions. Then the method will be used to estimate the NNMs of a curved steel beam that exhibits significant modal interactions. The results will be validated against those obtained using well-established testing approaches.