Vibration energy transfer in nonlinear coupled near-identical systems

Abstract

Near-identical systems (NIS) are widely encountered in practical engineering applications, where nominally identical substructures inevitably exhibit small deviations due to manufacturing tolerances, assembly imperfections, operational wear, or local damage. These minor variations can lead to pronounced changes in vibration behaviour, energy redistribution, and dynamic performance, particularly in coupled and cyclically symmetric structures. Understanding the vibration energy transfer mechanisms in NIS is important for vibration control, mistuning assessment, and structural health monitoring. This thesis presents a systematic investigation of vibration dynamics and energy transmission in NIS by integrating analytical modelling, numerical simulation, and experimental validation within a power flow analysis (PFA) framework. The study begins with 2-DOF coupled oscillator and beam systems, where the power flow mechanisms induced by small parameter deviations are revealed. It is shown that power flow analysis provides clear physical insight into directional energy transfer and frequency dependent energy redistribution that cannot be fully captured by conventional response-based approaches. The effects of nonlinear coupling on vibration response and energy transmission are further examined, demonstrating the emergence of multi-valued responses and altered power flow patterns.
The proposed framework is subsequently extended to more complex systems, including multi-DOF arrays and nonlinear mistuned bladed disk systems. A lumped parameter model (LPM) incorporating cubic stiffness and dry friction nonlinearities is developed to capture blade-disk interactions. The results demonstrate that cubic stiffness enhances blade-to-disk energy transfer and promotes resonance shifts, while dry friction primarily dissipates vibration energy and suppresses excessive response amplitudes. Power flow-based indicators are shown to be effective in quantifying mistuning sensitivity and identifying critical design parameters. Extensive experimental investigations are conducted to validate the theoretical and numerical findings. Impact hammer testing, shaker excitation, and scanning laser Doppler vibrometer are employed to study near-identical beam systems, bladed disks, and blisk structures. The experimental results confirm both the global and local effects of small deviations and defects on vibration characteristics, including energy localization, mode splitting, and amplitude redistribution.
Overall, this thesis establishes a comprehensive analytical-numerical-experimental framework for investigating vibration power transfer in NIS. The methodologies developed the fundamental understanding of power flow mechanisms and provide practical tools for vibration suppression, mistuning evaluation, and structural health monitoring in a wide range of engineering applications.

Date of Award	18 Jul 2026
Original language	English
Awarding Institution	University of Nottingham
Supervisor	Jian Yang (Supervisor) & Xin Dong (Supervisor)