Adaptive nonlinear vibration absorbers for uncertain rotating machinery structures

This paper introduces an adaptive nonlinear vibration absorber (NVA) for mitigating vibrations in rotating machinery subjected to parametric uncertainty. The coupled shaft-absorber system is modelled using a nonlinear mass-spring-damper framework, and the governing equations of motion are derived via the Euler-Lagrange approach. Uncertainty in the shaft properties is incorporated through a stochastic formulation, and statistical linearisation is employed to obtain tractable frequency domain representations. Closed-form optimal tuning parameters are derived using H2 optimisation, while H∞ optimisation is further utilised to enhance robustness against worst-case dynamic responses. The novel NVA integrates nonlinear stiffness characteristics to achieve broadband vibration suppression and reduced sensitivity to mistuning. Monte Carlo simulations are performed to evaluate system performance under uncertainty, demonstrating a vibration reduction capacity of 27.45% in the frequency domain and 3.37% in the time domain. The results show that the NVA consistently outperforms conventional tuned mass dampers by providing lower peak responses, faster transient decay, and improved robustness for a stochastic perturbation level of ε = 0.2. Overall, this paper establishes the adaptive nonlinear absorber as a reliable and efficient solution for vibration control in uncertain rotating systems, with strong potential for practical implementation in advanced engineering applications.