This study systematically investigates the global coupled response characteristics and stability transitions of a piecewise-smooth rotor/stator system subject to multiple synergistic non-smooth and continuous nonlinearities, including geometrical nonlinearity, non-smooth rubbing constraints, cross-coupling stiffness and dry friction forces. Based on perturbation theory, a piecewise analytical bifurcation framework is developed to delineate the global response characteristics. Explicit analytical existence boundaries for no-rub motion, synchronous full annular rub, partial rub, and dry friction backward whirl are formulated. Results reveal a sophisticated topological map featuring seven distinct coexistence regions, notably multiple triple-stability zones where benign and catastrophic attractors coexist. Critically, a codimension-2 Fold-Hopf bifurcation is identified as the topological nexus driving the transition from bi-stability to high-order multi-stability. Beyond this threshold, severe attractor clustering emerges, rendering the system highly sensitive to initial conditions. Furthermore, it is demonstrated that the hardening characteristic of geometric nonlinear stiffness effectively suppresses destructive backward whirl and partial rub. The proposed analytical methodology is scalable to the piecewise smooth rotor/stator systems with higher-order elastic restoring forces, offering a generalized paradigm for elucidating the dynamical evolution of complicated rubbing responses.
This paper studies resilient consensus of discrete-time nonlinear multi-agent systems subject to unmatched unknown inputs, bounded sensor noise, and mixed Denial-of-Service (DoS) and False Data Injection (FDI) attacks. The nonlinearities are described by Incremental Quadratic Constraints (IQCs). To relax structural restrictions on existing IQC multiplier matrices, a projection-lemma-based Unknown Input Observer (UIO) is developed to decouple the unknown inputs under a rank condition and yield a convex sufficient observer-design condition. The observer also provides a one-step-delayed input reconstruction with an explicit noise-dependent error bound. This bound is incorporated into a zonotope-based set-membership detector that combines localized interval-Jacobian enclosures and sliding-window generator reduction to limit reachable-set inflation. For unavailable or isolated links, a predictor supplies surrogate neighbor information, while dynamic trust weights reduce the influence of increasingly uncertain predictions and redistribute weight to available neighbors. Under the stated rank, bounded-uncertainty, healthy-neighbor, and average-dwell-time conditions, the consensus error is shown to be uniformly ultimately bounded. Simulations with saturated polynomial, sinusoidal, and hyperbolic-tangent nonlinearities illustrate, for the tested scenarios, the detector response, bounded control effort, and trust-weight evolution.
Predefined-time (PdT) synchronous navigation is essential for the cooperative operation of unmanned surface vessels (USVs), as it guarantees rapid formation recovery and precise coordination under stringent temporal constraints. In practice, however, this objective is severely challenged by the concurrent presence of unknown ocean disturbances, model uncertainties, and unavailable leader velocity–factors that jointly undermine disturbance-rejection accuracy and invalidate conventional synchronization schemes. To counteract these obstacles, we develop a PdT precise anti-disturbance synchronous navigation control framework comprising three core components: a PdT nonlinear disturbance observer (enhanced by an auxiliary dynamic system) for accurate estimation of lumped uncertainties; a PdT velocity estimator that recovers the leader’s velocity within a PdT without direct measurements; and a PdT synchronous navigation controller, synthesized via backstepping, that ensures global PdT stability. The effectiveness and practicality of the proposed strategy are substantiated through simulations on a representative USV model.
Self-excited vibration (SEV), often induced by spline misalignment and tooth friction in spline-connected driveshaft systems, poses a severe threat to rotor system operational safety. Consequently, a reliability assessment is imperative. This paper presents a reliability analysis framework for floating spline-connected driveshaft systems based on the nonlinear dynamic response of the rotor, using the Bayes formula in conjunction with the AK-MCS (B-AK-MCS) method. A finite element dynamic model of the floating spline-connected driveshaft system is established, incorporating analytical spline nonlinear stiffness and friction torque models, and validated against experimental results obtained from a spline-connected driveshaft test rig. Self-excited vibration is treated as the system failure mode, and limit state functions are formulated based on the vibration amplitude thresholds of the shaft. The failure probability function (FPF) is efficiently computed via B-AK-MCS in a single reliability assessment. Four uncertainty cases are systematically investigated, considering the spline friction coefficient, coupling angular stiffness, coupling lateral stiffness and support lateral stiffness as random inputs. It is revealed that the spline friction coefficient and coupling angular stiffness are the dominant sensitive parameters governing SEV onset. Bifurcation analysis demonstrates that these critical parameters exhibit distinct bifurcation points beyond which the system transitions abruptly from period-1 motion to quasi-periodic motion. The proposed framework provides theoretical guidance for the reliability-oriented design of floating spline-connected driveshaft systems.
The traditional nonlinear energy sink (NES) consists of an essentially nonlinear spring, which can be difficult to realize in practical implementations. In this study, three variant NESs without an essentially nonlinear spring are designed and compared with a target cubic NES: a mono-stable NES (MNES), a bi-stable NES (BNES), and a tri-stable NES (TNES). A finite-amplitude equivalent-stiffness design framework is proposed in which the restoring force of each variant NES is matched to that of the target NES at a prescribed reference displacement. The resulting representative designs are evaluated for transient vibration suppression and simultaneous vibration-suppression/energy-harvesting trade-offs using piezoelectric and electromagnetic energy harvesters. For the steady-state harmonically forced case, the electromagnetic-harvester-equipped systems are formulated using a normalized harmonic-balance approach implemented with NLvib. An auxiliary electrical coordinate is introduced to express the electromagnetic current equation in a second-order form suitable for continuation, and Hill-based stability analysis with Floquet-exponent filtering is used to classify the computed periodic branches. Direct time integration is used to validate the harmonic-balance frequency responses and to interpret modulated responses near unstable resonance-region branches. Multiobjective optimization is then performed over operating conditions, and additional sensitivity studies are added to examine the dependence of the reported rankings on the reference displacement and design-specific absorber parameters. The results show that no single NES configuration is universally preferred. For the selected equivalent-stiffness parameter sets, the BNES provides strong low-energy transient performance, while the preferred steady-state configuration depends on the excitation regime and on the relative priority assigned to vibration suppression and energy harvesting. The comparison between PEH and EMEH is likewise conditional on the adopted harvester parameters.
