Nonlinear Normal Mode backbone estimation with near-resonant steady state inputs

Abstract

This work presents a new technique for nonlinear system identification that utilizes near-resonant steady-state harmonically excited vibration measurements to estimate the Nonlinear Normal Mode backbones. The algorithm is based on the previously proposed Single Nonlinear Resonant Mode formula and uses it in a new and more effective way to estimate one point on the nonlinear mode from only one steady-state measurement collected near the resonance. A by-product of this work is a derivation of a novel formula expressing how the damping ratio changes with the motion amplitude. Several measurements at various forcing amplitudes can be combined to estimate the nonlinear mode and damping as a function of amplitude, which can be further used to predict the forced steady-state response of the structure in the vicinity of the mode of interest. Compared to existing phase resonance methods, the proposed technique can reduce the time required to obtain measurements and avoids difficulties due to e.g. the premature jump phenomenon. The algorithm assumes that the modes are well-separated and no internal resonances are present in the system. Additionally, it requires the accurate identification of linear modes in the low-amplitude vibration tests and it assumes that the nonlinear normal mode shape does not change significantly with response amplitude The method is first evaluated numerically using reduced models of clamped–clamped flat and curved beams that exhibit both stiffening and softening–stiffening responses, respectively. Then the method is employed experimentally to measure the NNM backbones of beams that were manufactured from polylactide using a 3D printer and experience significant eigen-frequency shifts when the motion amplitude increases. The results are validated against measurements collected using the traditional phase resonance testing approach.