Wei Sun

We present a new gyroscopic rotor dynamic model that rigorously captures lateral vibrations of flexible rotating shafts. The model treats the rotor as a stepped Euler–Bernoulli beam with spring supported bearings, concentrated disk masses and rotary inertias. Unlike conventional approaches, our formulation demonstrates that two plane coupling during whirling arises fundamentally from centrifugal and Coriolis forces rather than simplified gyroscopic inertia terms. The resulting coupled partial differential equations are solved analytically via Laplace transformation and Cauchy’s residue theorem, yielding exact closed form expressions for whirling frequencies, critical speeds and unbalance responses. The solutions reveal previously unrecognised intrinsic behaviours, including continuous variation of whirling frequencies with spin speed across all bending modes. Numerical examples and comparisons with finite element predictions highlight limitations of traditional methods and emphasise the need for more precise theoretical models in high speed rotor design. This work therefore bridges the gap between rigorous analytical theory and practical rotor dynamics applications, providing a robust benchmark and a design oriented framework for predicting, understanding and mitigating gyroscopic vibration phenomena.

Strength assessment for thermal barrier coatings (TBCs) is vital in the safety design of hot-section components in engines. However, several crucial factors, including thermally grown oxide (TGO) growth and creep–plasticity interaction, have been less considered in thermo-mechanical analyses for TBCs near air holes. In this study, a unified viscoplastic constitutive model incorporating TGO growth is developed and integrated into a finite element framework. The model considers multiple factors, including TGO growth, creep–plasticity interaction, interface undulation, and temperature gradient. Additionally, an analytical solution for the non-uniform temperature field of a TBC is derived. The model is then applied to calculate interfacial stresses and accumulated strain energies in the TBC near an air hole, which promote interface debonding. The obtained results can be utilized to investigate the mechanisms of hole edge delamination in TBCs, considering the combined effects of multiple complex factors. A competition for the potential failure initiation location is revealed between the first oxide layer and the evolving TGO/bond coat interface. The developed viscoplasticity model demonstrates effective capability in modelling a range of dynamic behaviors that collectively contribute to hole edge delamination failure.