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

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