Modern permanent magnet marine auxiliary equipment is lighter and more compact with equal power output. Traditional vibration assessment indices cannot accurately evaluate its vibration performance. This paper presents a targeted vibration transmission analysis method, laying a theoretical framework for vibration evaluation of lightweight marine equipment.

To achieve this objective, a multi-step research framework was adopted. First, the power machinery and its vibration isolator were simplified into a single-degree-of-freedom (SDOF) system mounted on an elastic foundation. The equivalent parameters of the mass-spring-damper model were determined based on the equipment's mass characteristics and the impedance properties of the isolator. Under the conditions of constant installation frequency and unchanged input impedance of the elastic foundation, the system's dynamic equations were formulated to reveal the underlying mechanism governing the relationship between equipment mass and vibration transmission characteristics. Second, power flow analysis was employed as the primary metric for evaluating vibration energy transmission. Mathematical derivations were performed to establish the quantitative relationships between the equipment mass and both the foot vibration acceleration level and the vibration power flow transmitted to the base. Furthermore, numerical simulations and case validations were conducted using two types of base structures with different impedance characteristics: a simply supported rectangular plate (1 m × 1 m × 2 mm) and a typical marine bench base (with specific dimensions, such as a top plate area of 0.62 m × 0.43 m). Finite element analysis (FEA) was performed to compute the input velocity impedance and output power within the frequency range of 10–1 000 Hz, thereby verifying the theoretical derivations. Finally, a bench test was conducted using an IRG 32-125 centrifugal pump, to which additional masses were added to create three configurations with different masses (41.5, 71.5, 111.5 kg), each paired with BE-series vibration isolators. Acceleration sensors and force hammer excitation were used to collect vibration data, and the power flow was calculated using the four-pole parameter method to validate the theoretical and simulation results.

The results consistently demonstrated several key patterns. Under the conditions of constant installation frequency and base impedance, a reduction in equipment mass led to an increase in the foot vibration acceleration level while enhancing the overall vibration isolation performance. Specifically, at the first-order resonance frequency, the peak active power flow transmitted to the base increased with decreasing mass – showing gains of 5.97 and 20 dB corresponding to 50% and 90% mass reductions, respectively. Similarly, the foot vibration acceleration showed a significant upward trend: it increased by 1.97 times for a 50% mass reduction and by 9.98 times for a 90% reduction. Meanwhile, the acceleration level drop (i.e., the difference between the foot acceleration level and the base acceleration level) also increased with decreasing mass, indicating improved vibration isolation performance. The bench test results aligned with the theoretical and simulation outcomes. For the three mass configurations, the foot acceleration levels were 163.07, 153.36, and 144.63 dB respectively, while the corresponding acceleration level drops were 43.36, 30.75, and 25.30 dB. These findings confirmed the trend of improved isolation performance with reduced mass. Additionally, the power flow at the lower end of the vibration isolator increased as the equipment mass decreased, further validating the theoretical relationship between equipment mass and vibration energy transmission proposed in this study.

This study explores vibration transmission of lightweight auxiliary equipment with fixed installation frequency and base impedance. Equipment mass is key to the peak power flow at the base’s first natural frequency, showing an inverse correlation: lower mass brings markedly higher peak power flow. Although reduced mass increases foot vibration acceleration, it enhances vibration isolation with larger acceleration attenuation. Compared with the traditional foot acceleration level, power flow based on energy transmission is a more rational index to evaluate the acoustic performance of lightweight permanent magnet auxiliary equipment. In engineering, the acceleration criteria can be properly relaxed, and power flow evaluation helps maximize the benefits of lightweight design. This work offers theoretical support for vibration isolation design and performance assessment, advancing the application of such equipment in vehicles.

Laser scanning technology used in the intelligent installation of ship shafting has such advantages as non-contact, high-speed scanning and high-precision imaging. The laser point cloud data includes the size, position and direction information of space objects. Point cloud segmentation can greatly reduce the calculation scale of the data and improve the measurement efficiency of the relative pose of the butt flange.

In this paper, deep learning theory is used to study point cloud segmentation and obtain a point cloud dataset of flange parts. The PointNet model is used for training. Optimization strategies are formulated in three aspects, namely dropout regularization, learning rate attenuation and point cloud data enhancement, then tested on a ship shafting intelligent installation platform.

The convergence results of the model tend to be stable, with the accuracy of the training set reaching 0.88 and that of the verification set reaching 0.65. The flange point cloud segmentation experiment shows clear contour edges.

The results of this study show that the proposed method has good convergence and generalization performance, and can improve the efficiency of ship shafting intelligent installation.

In order to reduce the influence of ship service life extension uncertainty and fatigue risk during future service life extension, a dynamic maintenance sequence decision based on the real option analysis method is adopted.

The local fatigue of a high-speed ship is taken as an example. This strategy strengthens the maintenance in the early stages of the ship's service and determines the adaptive maintenance decision according to the requirements of service life extension in the later stages, thereby adapting to the various possibilities of service life extension in the future.

Compared with the traditional maintenance strategy, the flexible decision under real option analysis can reduce the influence of service life extension uncertainty and effectively reduce failure risk during service life extension.

The sequential decision made via the real option analysis method has strong adaptability to the uncertainty of service life extension in the future and provides a new idea for maintenance decisions.

This paper aims to study the free vibration characteristics of complicated shape plate coupled with fluid under elastic boundary conditions.

To this end, the rectangular domain enveloping the complicated shape plate domain is selected, and the plate displacement is expressed by the improved Fourier series in the rectangular domain. Combined with the Rayleigh integral, the relationship between the plate displacement and the surface sound pressure is established, and the integral formula is transformed into polar coordinates to avoid singularity. Aiming at the problem that it is difficult to obtain the explicit expression of the boundary curve in the variable limit integral in local polar coordinates, the structural boundary curves are treated by "replacing curve with straight" to simplify the Rayleigh integral. Based on the energy principle, a semi analytical method for analyzing the free vibration characteristics of complicated shape plate contacting with water on one side is established.

The numerical examples of rectangular plate, circular plate and some complicated shape plates are given. Compared with the finite element method and literature results, the convergence and accuracy of the method are verified, and the influence of elastic boundary conditions on the added virtual mass incremental (AVMI) factor of plate is discussed. The AVMI factor of each mode reaches the maximum near the dimensionless displacement spring stiffness of 10³. At this time, the structure is relatively most affected by the fluid.

This method has strong adaptability and high calculation efficiency. It reveals the free vibration law of complicated shape plate coupled with fluid, and has certain engineering guiding significance.

In view of the insufficient safety and reliability of the traditional deterministic vibration analysis of ship propulsion shafting system, the vibration response analysis of the shafting system under uncertain excitation conditions is carried out.

Using non-random vibration analysis based on non-probabilistic convex model process, the uncertain excitation and vibration response are described in the form of the upper and lower bounds of the interval to reduce dependence on a large amount of excitation sample data. Compared with the calculation results in the relevant literature, the validity of the program for solving the response bound of the two-degrees-of-freedom (2-DOFs) system is verified, and the uncertain vibration problem of the shafting system is then explored on this basis.

The results show that when the shafting system is excited by [−30 N, 30 N] propeller laterally, a displacement response of the magnitude of about 10⁻⁶ m is generated at the bearing. It is also indicate that the shafting system is excited in a certain interval, so a certain interval response must be produced.

Applying the non-probabilistic convex model process and non-random vibration analysis to the field of the uncertain vibration analysis of ship propulsion shafting system, the vibration displacement response bound of the shafting under uncertain excitation conditions can be obtained with fewer excitation samples, thereby providing useful references for improving the robustness of the dynamic response prediction of ship propulsion shafting systems.

Due to the larger length-to-diameter ratio of the stern bearing, it is difficult to reflect its actual operating conditions when simplified to the traditional equivalent model of single-point support. Therefore, the influence of the equivalent form of the stern bearing on the transverse vibration characteristics of the shafting is investigated.

The improved Fourier series is introduced to describe the lateral vibration displacement of propulsion shafting. Then, the calculation model of lateral vibration performance of propulsion shafting under various equivalent forms, such as single-point support, multi-point support or continuous distributed support, are constructed based on the energy principle. Thereby, the influence of the change of support stiffness equivalent to the liquid film pressure on the lateral vibration of the shafting and the influence of the propeller excitation on the vibration response of the shafting are further analyzed. Finally, the results acquired by the proposed model is compared with the results of related references and finite element method (FEM) to verify the validity of the calculation model.

The multi-point support calculation results converge to the continuous distributed support calculation results. The three-point support equivalent form can be used to study the influence of liquid film pressure distribution on the lateral vibration characteristics of the propulsion shafting. The shafting response under propeller excitation is affected by the revolution speed.

The research indicates that three-point support equivalent form can be used to analyze the influence of liquid film pressure on the shafting lateral vibration performance. The proposed model in this paper has advantages of good convergence, high accuracy, and less cost-consuming.