With the rapid development of precision instruments, aerospace, and automotive industries, the demand for compact vibration isolators capable of suppressing low-frequency vibrations has surged. Although prior reviews have established the theoretical framework of quasi-zero stiffness (QZS) isolators, critical gaps persist in addressing their compact design under strong nonlinear dynamics and diverse engineering constraints. This review systematically analyzes the dynamic characteristics of QZS systems under nonlinear effects and evaluates five innovative design methodologies for compact QZS isolators: special spring type, magnetic type, bionic type, metamaterials-based type, and origami-inspired type. Key findings reveal that special spring-type isolators are simple to design and space-efficient but difficult to machine. Magnetic-type isolators achieve ultra-low start-up frequencies but face thermal instability. Metamaterial designs enable multifunctional integration at the cost of manufacturing complexity, while bionic-inspired and origami-inspired isolators are difficult to abstract for practical applications. We find that current research tends to prioritize miniaturization over the synergistic optimization of load capacity, broadband isolation, and adaptability. Future research should focus on multi-degree-of-freedom systems, coupled metamaterials-bionic structures, and active magnetic control. This work provides a key roadmap for advancing compact QZS technology in space-constrained applications.

Vibration is a critical issue in aerospace structures, where lightweight design, high flexibility, and complex operational environments often lead to pronounced nonlinear dynamic responses. Excessive vibrations induced by harmonic excitations, aerodynamic loads, or onboard equipment can significantly degrade structural integrity, control accuracy, and service life. Consequently, advanced passive vibration suppression techniques with strong robustness and broadband effectiveness are of great importance in aerospace engineering applications. The bifurcation boundary and vibration suppression performance of Piezoelectric–Monostable Nonlinear Energy Sink (PMNES) are crucial for evaluating its effectiveness on the main structure. To simplify the analysis of flexible aerospace structures, a reduced-order model is derived by modal truncation in the low-frequency range, which is then treated as a two-degree-of-freedom main structure. To focus on the underlying nonlinear dynamic mechanisms, an equivalent two-degree-of-freedom lumped-parameter system is adopted as a generic representation of the dominant low-frequency dynamics of flexible aerospace structures. In this work, the electromechanical coupling control equations of the system of a two-degree-of-freedom main structure coupled with PNES are derived through the application of Newton’s second law and Kirchhoff’s voltage law. The methods of complexification-averaging (CX-A) and Runge–Kutta (RK) are employed to assess the vibration suppression performance and stability characteristics of the system under harmonic excitation. The approximate solution is validated through numerical solutions. The approximate solutions of the system are employed to derive the Saddle Node (SN) bifurcation and codimension-two cusp bifurcation points, while the enhanced algorithm is employed to ascertain the most unfavorable amplitude at each external excitation circular frequency and to determine whether the mark represents a Hopf Bifurcation (HB) point. The generalized transmissibility is utilized to assess the efficacy of vibration suppression. The various vibration suppression efficiency regions are created by superimposing the vibration suppression efficiency maps and bifurcation maps. The influence of PNES parameters on the vibration suppression region is investigated. The results indicate that this method can effectively evaluate the bifurcation boundary and vibration suppression performance of PMNES.

To address the detuning sensitivity of conventional linear vibration absorbers under wide-frequency harmonic excitation and the limited effectiveness of nonlinear energy sinks (NESs) in low-energy regimes, this study investigates a bistable nonlinear energy sink (BNES) based on a negative-stiffness support. A coupled model of the primary system and the BNES is established, and the analytical steady-state amplitude–frequency relationship of the system is derived using the harmonic balance method. The accuracy of the analytical solutions is verified through numerical integration. Based on the first Lyapunov method, the instability regions of the system are identified, and the effects of system parameters on the amplitude–frequency response of the primary structure are analyzed. On this basis, a comprehensive performance index that accounts for both peak suppression and average vibration reduction over the frequency band is constructed, and an improved particle swarm optimization algorithm is employed for parameter optimization. The results demonstrate that the optimized BNES can effectively suppress isolated high-amplitude response branches and significantly reduce the response of the primary system within the resonance frequency band, exhibiting superior broadband vibration mitigation performance and enhanced stability.

This study investigates the hydrodynamic performance of the KVLCC2 tanker in deep and shallow water using computational fluid dynamics (CFD) simulations, focusing on resistance and self-propulsion with both ducted and non-ducted propellers. The Reynolds-averaged Navier–Stokes (RANS) equations, coupled with the SST k-ω turbulence model, are solved using STAR-CCM+ to analyze ship resistance, open-water propeller characteristics, and self-propulsion factors. Validation against experimental data confirms the numerical accuracy, with uncertainties below acceptable thresholds. In deep water, the body force propeller and body force ducted propeller methods are validated against the discretized propeller approach, yielding errors under 5%. The ducted propeller enhances open-water efficiency but results in higher thrust deduction and lower wake fractions, leading to reduced hull and overall propulsive efficiencies compared to the non-ducted case. In shallow water, as the depth-to-draft ratio (H/T) decreases to 1.5, added resistance, sinkage, and trim increase sharply due to blockage effects. The ducted configuration mitigates these penalties, achieving a 20.8% power reduction at H/T = 1.5. Added self-propulsion factors reveal that the duct improves hull efficiency and offsets shallow-water losses, enhancing propulsive efficiency. Flow field analysis shows accelerated stern wakes and asymmetric structures in shallow water, with the body force methods providing consistent predictions despite minor discrepancies in extreme conditions. This research highlights the efficacy of ducted propellers in shallow water and the reliability of body force methods for efficient simulations, offering insights for ship design in restricted depths.

This study proposes a permanent magnet edge topology optimization method to address the low force output efficiency in Electromagnetic Vibration Absorbers caused by magnetic field distortion at the geometric discontinuity between the permanent magnet and the magnetic yoke. A theoretical model incorporating magnetic flux enhancement and improved directional consistency is established, revealing a transition in dominant mechanisms: magnetic flux enhancement dominates at small chamfer depths, while improved directional consistency becomes predominant at larger chamfer depths. Experimental validation was conducted on the optimized structure with a standard chamfer angle and 4 mm chamfer depth under operational conditions. Test results show an average force output increase of 4.6%, reaching 6.8% at 5 A. This research provides a theoretical basis and design methodology for geometric optimization of electromagnetic actuators in space-constrained environments.