In recent decades, quasi-zero stiffness (QZS) vibration isolation systems with nonlinear characteristics have aroused widespread attention and strong research interest due to their enormous potential in low-frequency vibration isolation. This work comprehensively reviews recent research on QZS vibration isolators with a focus on the principle, structural design, and vibration isolation performance of various types of QZS vibration isolators. The negative-stiffness mechanism falls into two categories by different realization methods: passive and active/semi-active negative-stiffness mechanisms. Representative design, performance analysis, and practical application are elaborated for each category. The results show that passive vibration isolation systems have excellent low-frequency vibration isolation performance under specific payload and design parameters, whereas active/semi-active vibration isolation systems can better adapt to different environmental conditions. Finally, the development trends and challenges of QZS vibration isolators are summarized, and the solved and unsolved problems are highlighted. This review aims to give a comprehensive understanding of the QZS vibration isolation mechanism. It also provides guidance on designing new QZS vibration isolators for improving their vibration isolation performance and engineering applicability.

The propulsion shaft system, as the core of the ship’s power system, has attracted widespread attention in terms of vibration. This paper is dedicated to the study of the dynamic response characteristics of the ship propulsion shafting system, with a particular focus on the impact of the shaft-driven generator supported by bearings on the dynamic torque of the shafting system. A classic lumped-parameter equivalent system model is adopted, and the time domain transient response simulation calculation is conducted based on the Newmark-β method. A comprehensive analysis is made of the vibration torque and vibration stress in the propulsion shaft system under different rotational speeds and working conditions, with or without the shaft-driven generator connected to the load. Dynamic vibration torque measurements are also taken on a 16100TEU ship for the propulsion shaft system to analyze the consistency between simulation results and experimental results. The results show that at the rated speed of the main engine at 80 rpm and adjacent speeds, the error between the simulation calculation results and the actual measured torque results at the pre- and post-motor measurement points is less than 10% and is much less than the continuous allowable torque of 4.01 × 10⁶ N·m and the instantaneous torque. This installation state, including the propulsion shaft system with the shaft-driven generator supported by bearings, can safely navigate during normal operation. This provides theoretical and experimental support for the future installation of the propulsion shaft system with the shaft-driven generator supported by bearings. In addition, the actual ship experiment enhances the universality and reliability of the research.

In order to effectively control the low-frequency vibration of ship machinery, based on the improved multi-line spectrum adaptive control algorithm, a two-degree-of-freedom (two-DOF) active-passive hybrid vibration isolator composed of an electromagnetic actuator, rubber spring, and the hydraulic device is proposed. The dynamic model of the two-DOF vibration isolation system is established and the main control force demand of the vibration isolation system at different damping forces is analyzed. By introducing the improved wavelet packet decomposition algorithm with the Hartley block least mean square algorithm to the filter-x least mean square (FxLMS) algorithm, an improved wavelet packet Hartley block filter-x least mean square (IWPHB-FxLMS) algorithm is established. The experimental results show that the IWPHB-FxLMS algorithm has better control performance. Compared with the traditional FxLMS algorithm, the IWPHB-FxLMS control algorithm improves the convergence speed by 91.7% and the line spectrum power spectrum attenuation by 58.1%. The active-passive hybrid vibration isolator is based on multi-line spectrum adaptive control and can achieve good control effects under the excitation of multi-frequency line spectrum and constant frequency line spectrum.

Nonlinear energy sink (NES) systems, when applied to a physical system with multiple interference sources, exhibit abundant nonlinear dynamic behaviors. However, current research in this respect is limited within the theoretical scope of deterministic systems. According to the theory of cell mapping, this paper introduces a parallel restructured algorithm to improve the performance of cell mapping and cell processing, and a parallelized multidegrees-of-freedom (DOF) cell mapping (PMDCM) method is given. With the method, the global behavior of NES systems is analyzed so that the dynamical behavior of multiple stable attractors within typical parameter intervals can be captured. The research results show that for NES systems, there is the phenomenon of multiple stable attractors coexisting in multiple typical parameter intervals, which occurs between periodic and periodic attractor, periodic and quasi-periodic, periodic and chaotic attractor. While revealing the corresponding relationship between different types of attractors and their basin of attraction, these findings verify that the new cell mapping method has high computational efficiency and accuracy and can provide a theoretical basis for the study of high-dimensional nonlinear systems' global behavior and optimal control.

In research concerning the impact resistance characteristics of ship power transmission shaft systems incorporating a high-elasticity coupling, a significant challenge lies in ascertaining the displacement compensation metrics for the high-elasticity coupling. This study constructs a finite element model of the ship power transmission shaft system with an entity equivalent model of the high-elasticity coupling. Utilizing the Dynamic Design Analysis Method (DDAM) and the time-history method, the dynamic responses of the high-elasticity coupling, the propulsion shaft system, and its critical cross-sections under explosive impact loads are analyzed. The findings indicate that the maximum impact displacement of the propulsion shafting system, as calculated by DDAM, is 22.47 mm in the vertical direction at the driven end of the high-elasticity coupling. In contrast, the maximum impact displacement determined by the time-history method is 15.23 mm in the same direction. The study corroborates the precision of the high-elasticity coupling equivalent model establishment methodology and confirms that the entity equivalent model of the power transmission shaft system with a high-elasticity coupling is capable of fulfilling the criteria for a swift evaluation of impact resistance characteristics. This provides theoretical backing for the forecasting of impact resistance performance in ship propulsion shaft systems.