Aiming at the complex vibration modes and excessive number of modal test points in underwater vehicle stern structures, this paper proposes an optimal sensor placement method.

First, a finite-element model of a typical stern structure is constructed using S3 and S4R plate elements to simulate the structure's shell and rib plates. Subsequently, the structural parameters, such as nodes, elements, and the stiffness and mass matrices are extracted from the model file. To optimize sensor placement, a composite objective function is constructed by integrating a three-dimensional redundancy elimination index and the modal assurance criterion (MAC). The three-dimensional redundancy elimination index ensures adequate spatial separation between sensors in each direction and from the center of the stern structure. The MAC helps maintain the linear independence of modal shapes. Then, the GA−BPSO algorithm is employed to optimize sensor placement using binary coding. Each particle in the particle-swarm algorithm represents a placement plan, with its dimensionality corresponding to the number of candidate degrees of freedom. Each degree of freedom can either as 1 (sensor placed) or 0 (no sensor). The algorithm updates particle velocities and positions based on an inertia weight, learning factors, and random numbers. Positions are then discretized to 0 or 1 through a threshold. Genetic algorithm operators such as replication, crossover, and mutation are introduced to improve the performance of the binary discrete particle-swarm algorithm. The parameters of the GA−BPSO algorithm are carefully set. For example, the population size is set to 600, the number of iterations to 2 000, and the inertia weight decreases from 0.9 to 0.4 over the course of the iterations.

The optimized sensor layout reduces the number of required sensor locations from 840 (uniform layout) to 200. The maximum off-diagonal value in the MAC matrix in the optimized layout drops to 0.033 3, the frequency deviation remains below 1%, and the modal shapes show a high degree of consistency.

The proposed method effectively achieves a balance between the linear independence and visualization of modal shapes, demonstrating its applicability for modal testing of underwater stern structures.

To maximizing the working performance of the series-connected multi-sphere composite shell structure, an optimization design study has been conducted to enhance its acoustic and vibration performance.

First, a finite element model was developed to calculate and analyze the underwater acoustic radiation characteristics. Then, using the model's mass as the constraint condition and the radiation noise under vertical excitation as the optimization objective, a uniform experimental design was developed using the geometric parameters of the connecting structure as the design variables. The radial basis function (RBF) neural network was used to establish a multidimensional mapping model between the design variables and the optimization objective. The particle swarm optimization (PSO) algorithm was employed to optimize the underwater radiation noise of the model, and the results were verified through the finite element method. Finally, underwater acoustic radiation experiments were carried out, and the experimental test values were compared with the simulation values to validate the accuracy of the simulation results.

The results show that after optimization, the total underwater radiation sound power level of the series-connected multi-sphere composite shell under vertical excitation was reduced by 2.92 dB, while the mass was decreased by 0.061 t.

The research provides new insights into the optimization of low-noise structural design methods.

To address the challenges of heavy workload and long iterative cycles in the lightweight design of floating raft vibration isolation system in engineering applications, this study proposes a lightweight design method based on RBF-PSO multi-objective optimization algorithm.

Taking the plate-frame floating raft vibration isolation system as the research object, a finite element model was established using ANSYS APDL. The vibration isolation performance and impact resistance were evaluated through numerical simulation. Experimental tests were conducted to assess the vibration isolation performance of the floating raft. The accuracy of the numerical simulation was validated by comparing it with the experimental results. A full finite difference method was employed to analyze the parameter sensitivity of the floating raft vibration isolation system. Appropriate design variables were selected based on the sensitivity analysis. The lightweight design of the floating raft vibration isolation system was carried out using the RBF-PSO multi-objective optimization algorithm.

The results show that after optimization, the mass of the raft is 63.03 kg. Compared with the original design, the weight of the lightweight raft is reduced by 31.92%. The vibration isolation performance of the floating raft system improves by 2.48 dB. The impact resistance of the equipment is also improved. The discrepancy between the optimized result obtained by the RBF-PSO algorithm and the numerical simulation calculation is less than 1%.

Therefore, the RBF-PSO multi-objective optimization algorithm can be effectively applied to the lightweight design of the floating raft vibration isolation system.

To address the issue of nonlinear stiffness changes in isolation systems with limiters under impact excitation, an impact dynamics theoretical model and its anti-impact performance research are conducted.

First, using the idea of segmented linear equivalence, an impact dynamics theoretical model of a bidirectional limited single-layer vibration isolation system with a segmented linear stiffness limiter is established. The theoretical model is then solved using the analytical method and compared with the impact response of the finite element method under different impact conditions.

The analytical solution of the dynamic theoretical model is highly consistent with the finite element numerical solution under different impact conditions.

Through comparative analysis, the accuracy of the impact dynamics theoretical model and solution method of the bidirectional limited single-layer vibration isolation system with segmented linear stiffness limiter is verified, providing a theoretical basis for research on the working principle and performance characteristics of vibration isolation systems with limiters.

Due to the difficulty of accurately converting the experimental results of acoustic radiation and vibration from scale models of complex stiffened combined shells into prototypes, the acoustic vibration similarity laws of this type of combined shell are studied in order to provide a basis for scale model experimental research on the acoustic vibration of such underwater structures.

First, a complex stiffened cone-cylinder combined shell model and its scale model are constructed by shell element reinforcement simulation. Next, based on the hybrid finite element method-boundary element method (FEM-BEM) method, the acoustic vibration response of the combined shell is calculated. Combined with the model experiment, the accuracy of the calculated response of the complex shell structure using the hybrid FEM-BEM method is then verified. Finally, the acoustic vibration similarity laws of the complex stiffened cone-cylinder combined shell are studied systematically.

The vibration modal frequency of the complex combined shell is in inverse proportion to the geometric scale ratio with the model under the same material parameter boundary conditions and excitation force, while the vibration modal in the corresponding frequency is the same. Under conditions of the same excitation force, the vibration response of the combined shell is also in inverse proportion to the geometric scale ratio, whereas the acoustic pressure is in inverse proportion to the product of the geometric scale ratio and measurement distance of the shell. The radiation efficiency and acoustic directivity of the scale model and prototype are the same.

The stiffened cone-cylinder combined shell shows good acoustic and vibration similarity under similar conditions to those of the model, and the model constructed using shell element reinforcement simulation is more consistent with the experimental results.