Jun Jiang

Traditional analytical models for dry friction backward whirl predominantly rely on linear shaft assumptions, failing to capture amplitude-dependent frequency shifts and nonlinear response dynamics. For the geometrically nonlinear rotor/stator rubbing systems characterized by isotropic, smooth odd-polynomial restoring forces with arbitrary truncation orders, a generalized analytical framework for prediction of self-excited backward whirl is presented in this paper. By expanding the restoring force via a Taylor series with an arbitrary truncation order, a response decomposition strategy is established to treat the steady-state response as a superposition of a synchronous forced forward response and a self-excited backward whirl. A harmonic balance procedure is subsequently employed to decouple these components, yielding closed-form analytical solutions for both stability thresholds and orbital topologies. With the aid of numerical simulations, the proposed framework is validated across multiple degrees of nonlinearity, demonstrating excellent agreement with low root-mean-square errors when the relative sliding duration ratio exceeds 0.7. Crucially, compared with traditional linear rotors, geometric nonlinearity introduces a strong stiffness-hardening effect, resulting in reduced, self-limiting whirl amplitudes and pronounced upward frequency shifts. Furthermore, the instability boundaries of dry friction backward whirl and backward full-annular quasi-periodic rub are revealed to be governed by a nonlinear synergistic excitation driven by the dynamic coupling of dry friction, unbalance forces and geometric nonlinearity. This study provides a computationally efficient analytical tool capable of evaluating the physical qualitative trends and quantitative boundaries of nonlinear rotors for the stability assessment and vibration control of modern nonlinear rotor systems.

When adopting a viscous friction model in a piecewise nonlinear rotor–stator rubbing system, it becomes a Filippov system with smoothness of degree one. The nonautonomous system exhibits an interesting nonsmooth induced bifurcation phenomenon, that is, as the rotating speed increases, a quasi-periodic response emerges just after a periodic orbit of the linear sub-system touches the switching manifold, while the nonlinear sub-system possesses no regular periodic solution nearby. To investigate the mechanism of the nonsmooth induced bifurcation, the system is first transformed to the rotating coordinate system to get an equivalent autonomous system. Then, further transformations are performed to transform the system to an equivalent linear normal form in the neighborhood of the boundary equilibrium of the linear sub-system on the straightened switching manifold. After that, the Poincaré return map is constructed, and through numerical and analytical methods, it is shown that the tangency points of the two subsystems are mostly visible–invisible folds and invisible–invisible folds, and the system generates a limit cycle crossing the switching manifold. Through this analysis, the mechanism of the nonsmooth bifurcation in the original nonautonomous rotor–stator rubbing system is clarified. Moreover, the approximate model not only can accurately predict the maximum amplitude of quasi-periodic responses, but also reveal the coexistence of quasi-periodic and periodic motions. This highlights the usefulness of the proposed analytical approach for handling nonsmooth systems with engineering relevance.

The aim of this article is to present a novel intelligent fault diagnosis method based on the principle of stochastic resonance (SR) in array of noisy ReLU activators. To this end, the phenomenon of suprathreshold stochastic resonance (SSR), which is a resonance like collective effect of the array model for the input above threshold, is demonstrated, and the limit of the input-output relation of the average response is explicitly acquired. With the explicit noise intensity dependent relation as an activation function, the new fault diagnosis algorithm is proposed by training the intensity of Gaussian white noise as an independent parameter, and the corresponding initial value is set referring to the minimum point of the loss function defined by cross-entropy. A penalty term is further introduced to the loss function to ensure the nonnegativity of noise intensity. The performance and noise robustness of the proposed algorithms is validated by typical state-of-the-art networks across three open datasets, namely, CWRU bearing fault dataset, SEU gearbox dataset, and HUST varying speed gearbox dataset. It is found that the proposed algorithm outperforms its counterparts both in the absence of noise and in the presence of fixed noise on test accuracy. Particularly, the proposed algorithm can markedly improve the test accuracy when the training samples are limited and noise contaminated.

Collective behavior is among the most fascinating complex dynamics in coupled networks with applications in various fields. Recent works have shown that higher-order interactions widely exist in complex systems. Both positive couplings among nodes, as the majority of studies have assumed, and negative couplings are very common in real-world systems, like physiological networks. Positive coupling (excitatory coupling) promotes synchronization and drives excitatory synaptic transmission between neurons. Meanwhile, negative coupling (inhibitory coupling) inhibits synchronization and sustains inhibitory synaptic transmission between neurons. Since high-order coupling patterns and different coupling patterns strongly affect the synchronous performance of complex systems, this article develops a globally coupled higher-order oscillatory system model that incorporates both positive and negative couplings. It is shown that, in the case of positive couplings, a second-order interaction has a negligible impact on the synchronization capability of a network within a certain range. In contrast, a higher-order network with purely negative couplings exhibits asynchronous states for any values of the second-order interactions. However, the synchronous region gradually shrinks with the increase of the negative coupling in the case of mixed couplings. This indicates a prominent role of coupling patterns on the onset of globally higher-order network synchronization.