Enhanced nonlinear dynamics and monitoring bifurcation morphing for the identification of parameter variations

This paper proposes a novel vibration-based damage detection approach. The proposed technique is to actively change the stability of a fixed point (equilibrium state) of a system (structure) and create a new stable fixed point or limit cycle by applying a nonlinear feedback excitation. The nonlinear feedback excitation is designed such that a desired bifurcation (e.g., subcritical Hopf bifurcation) can occur, and a limit cycle may emerge close to the original fixed point. Hence, the deterioration of the structure during measurements is prevented, while the sensitivity of detection is increased by identifying the bifurcation point. The morphing of the bifurcation boundary (the locus of the bifurcation points) in the space of the controlled parameters of the nonlinear feedback excitation, together with the difference in the amplitude of the emerging limit cycle caused by the variation in structural parameters are utilized as features for the identification of parameter variations. To demonstrate the applicability and the potential (high sensitivity and robustness) offered by the proposed approach, a prototypical case of a two-degree-of-freedom mass-spring-damper system and a more complex example of a nonlinear panel forced by aerodynamic loads are investigated.