Conventional passive isolators provide limited low-frequency attenuation and face an inherent trade-off between load-bearing stiffness and vibration isolation. Inspired by the energy-absorbing and buffering mechanisms of coconut-shell layered structures, this study proposes a bio-inspired biphasic metamaterial isolator (BBMI). Its dispersion characteristics, bandgap mechanism, static and dynamic stiffness, and vibration attenuation are investigated through theoretical modeling, finite element simulations, prototype testing, and coupled-system analysis. The BBMI exhibits a complete broadband locally resonant bandgap, whose lower and upper boundaries are predicted by an equivalent lumped-parameter model with errors of 0.29% and 1.21%, respectively. Finite-array simulations confirm stable load-bearing stiffness and enhanced attenuation. Prototype tests yield an average bandgap attenuation of 53.8 dB, nearly twice that of an equal-sized rubber isolator. After optimization for marine equipment, the customized metamaterial isolator (CMI) achieves a 28.68-206.66 Hz bandgap and 20-40 dB transmission attenuation. Compared with the customized rubber isolator (CRI), the proposed isolator reduces the shell root-mean-square (RMS) velocity by over 30 dB and the underwater radiated sound power by 20-30 dB, demonstrating effective broadband low-frequency vibration and noise suppression.

To investigate the vibration transmission characteristics of the underwater shaft-cone-cylinder double-layer shell structure, a fluid-solid coupling finite element model was constructed based on the HyperMesh-ANSYS co-simulation platform, so as to simulate the full-process dynamic behavior of shaft excitation, bearing transmission, shell, and liquid coupling. The effects of interhull fluid density, bearing stiffness, and internal and external fluids of the shell on structural vibration transfer were systematically analyzed. The results show that the interhull liquid reduces the resonance frequency of the system through the added mass effect and enhances the sound pressure level through the fluid-solid coupling effect. The increase in bearing stiffness can suppress the shaft system vibration but excites the high-frequency resonance of the shell. In the low-frequency band, the strong continuity of the interhull liquid enhances the vibration transmission between the double-layer shells, while the additional mass and damping effects block the vibration transmission in the high-frequency band. This study reveals the vibration transfer effect of the underwater shaft-cone-cylinder double-layer shell model and provides theoretical support for the acoustic vibration design and vibration and noise reduction optimization of undersea vehicles.

Elastic metastructures with local resonance bandgaps exhibit promising prospects for low-frequency vibration suppression. However, most existing local resonance metastructures suffer from narrow bandgaps and complex material compositions, which limit their engineering application potential. To address this, a novel three-dimensional (3D) chiral metastructure with ultra-wide bandgap characteristics was designed in this study. A finite element model of the unit cell was established to systematically analyze its band structure and explored the influence of geometric and material parameters on the bandgap. The simulation results indicated that the unit cell generates local resonance effects through interactions between the chiral framework, connecting rods, and mass blocks. It not only achieves a lightweight design with a relative density of 0.341, but also realizes an ultra-wide bandgap with a relative bandwidth of 1.51, where the thickness of the chiral framework is the key parameter affecting the bandgap of the unit cell. Furthermore, the specimens were fabricated using laser melting technology, and random vibration tests were used to verify the reliability of the simulation results. Effective ultra-wideband vibration control was successfully achieved in the frequency range of 420.1-3032.5 Hz. The proposed 3D chiral metastructure provides a new solution for wideband vibration suppression and is expected to promote the widespread application of metastructures in practical engineering.

To resolve the inherent contradiction between low-frequency vibration attenuation and load-bearing performance in conventional metamaterials, this study proposes an innovative hybrid metamaterial design methodology. This method employs a Primitive-type triply periodic minimal surface (TPMS) structure fabricated via laser powder bed fusion (LPBF) as the load-bearing skeletal framework, within which local resonant units are embedded to achieve vibration attenuation. The bending wave bandgap, governed by local resonance mechanisms, yields significant vibration attenuation in the low-frequency domain, achieving a maximum transmission loss of 71.6 dB. Benefiting from its narrow-neck and wide-cavity topological configuration, the Primitive-type TPMS skeletal structure achieves synergistic optimization of both mechanical and vibration attenuation performance. In terms of load-bearing, its continuous and smooth curved surfaces enable uniform stress distribution and a stable compressive plateau stress. Regarding vibration attenuation, compared with the traditional box skeletal structure, the Primitive skeletal structure employed in this study can significantly broaden the bandwidth of the bandgap while maintaining the same parameters of the resonator. The key innovation lies in actively regulating the topological configuration of the skeletal structure, which enhances the effective mass ratio between the resonator and the matrix, thereby achieving a substantial broadening of the bandgap. Based on the designed metamaterial sandwich plate, a metamaterial floating raft is constructed and applied to the propulsion shaft-floating raft-hull coupled system of underwater vehicles. This metamaterial floating raft ensures structural bending rigidity while effectively mitigating the vibro-acoustic response of the hull surface, thereby enhancing the acoustic stealth performance of the vehicle. This research offers a new framework for designing metamaterial structures that combine load-bearing and vibration attenuation.

Research on the vibro-acoustic characteristics of the shaft-bearing-shell system holds considerable significance for developing low-noise underwater equipment. However, existing studies predominantly simplify bearings as linear spring models or adopt sequential solving methods for bearing lubrication and structural dynamics, overlooking the full extent of dynamic coupling effects between bearing lubrication and structural vibro-acoustic behaviors. To overcome these limitations, this study proposes a fully coupled dynamic modelling framework that integrates stern structure dynamics, bearing lubrication, and shaft alignment through a coupled feedback mechanism between the bearing and journal. This approach reveals the evolution law of the lubrication interface, while clarifying the mechanism by which bearing dynamic characteristics affect the vibro-acoustic responses of underwater vehicles. Results demonstrate that the dynamic alignment scheme incorporating bearing dynamic characteristics improves rear stern bearing lubrication and reduces stern structure vibro-acoustic response. Based on equivalent support point, the single-point support bearing model maintains accuracy and simultaneously enhance computational efficiency. Increased shaft hollowness reduces stiffness, worsening rear stern bearing lubrication and increasing structure vibro-acoustic response. Moreover, increasing the length-to-diameter ratio of each bearing can improve the lubrication conditions of the rear stern and intermediate bearings while suppressing the vibro-acoustic response, yet it may degrade the lubrication performance of the front stern bearing due to load redistribution. This study provides a theoretical basis for in-depth understanding of the stern structure vibration coupling mechanism of underwater vehicles.

This study proposes an analytical dynamic modeling method for the vibration analysis of trapezoidal plates under arbitrary boundary conditions. The method discretizes the trapezoidal plate into a series of narrow rectangular strips. Each strip is modeled based on the Kirchhoff plate theory and solved analytically, followed by global assembly through displacement compatibility and internal force equilibrium conditions. Combined with the artificial spring technique, this approach can flexibly simulate various complex constraint forms, including uniform and non-uniform, continuous and discrete, as well as elastic and rigid restraints. The effectiveness of the developed analytical dynamic model for trapezoidal plates is validated through finite element simulations and experimental tests. The research indicates that as the base angle increases, natural frequencies generally exhibit a declining trend, accompanied by mode exchange phenomena among lower-order modes, reflecting a modal competition effect induced by structure stiffness variation. Under point-supported boundary conditions, the normal stiffness has a significantly greater influence on natural frequencies than does the torsional stiffness. Line supports located in the mid-region of edges provide stronger constraint effects, whereas short supports closer to corners offer relatively limited constraints on low-order modes. In trapezoidal-rectangular combined plates, the thinner region dominates the lower-order modes and exhibits a stronger dynamic response. This study offers a theoretical basis for dynamic design and optimization of related engineering plate structures.

A novel analytic model is proposed for free vibration analysis of FGM non-coplanar plate assemblies with arbitrary boundary conditions. To establish the governing equation, the titled structures are firstly decomposed to several independent rectangular plates. The first-order shear deformation theory (FSDT) and the superposition method are employed, and both out-of-plane and in-plane displacements and forces are simultaneously expressed as some unknowns. Then, continuity conditions at coupling edges are utilized to assemble all plates, and displacements at other edges are restrained by artificial springs. By virtue of the orthonormal properties of trigonometric functions, continuity and boundary conditions become a series of algebraic equations, which are integrated to form the final governing equation. To evaluate the accuracy and application, natural frequencies of four different models are compared, and present results agree well with ones of the literature, finite element method and modal testing. Furthermore, influences of material parameters, elastic boundary conditions and discontinuity conditions are carried out. The results reveal that major differences between FGM and homogenous L-shaped plates are natural frequencies and mode shapes keep unchanged. The increase of coupling angle can efficiently increase natural frequencies as the coplanar plate becomes non-coplanar L-shaped one, and natural frequencies slightly change as the nonzero coupling angle further increases. Three discontinuity conditions including the coupling angle, coupling location and thickness can obviously affect natural frequencies of Lshaped plates.

Elastic metamaterials have achieved continuous breakthroughs in the field of structural vibration reduction engineering, owing to their distinctive capability of manipulating elastic waves. Nevertheless, the design of lightweight thin-plate structures that balance low-frequency broadband vibration suppression performance remains a challenge in structural engineering. Inspired by the rigid-flexible coupled vibration damping mechanisms inherent in biological systems, this study proposes a novel bionic lightweight elastic metamaterial thin plate without geometric discontinuity, which enables broadband vibration attenuation. A lumped mass theoretical analysis model was established, and a correction method for the rotational dispersion branch was proposed to accurately predict the bandgap boundaries. Furthermore, combined with the intrinsic modes of the start and end boundaries of the bandgap, equifrequency curves, group velocity, and phase velocity, the intrinsic driving mechanism that controls the opening and closing of the bandgap is analyzed in depth. Comprehensive quantitative analyses were performed to evaluate the regulatory effects of damping and geometric parameters on the bandgap characteristics and vibration transmission behaviors, thereby revealing the sensitivity of key parameters affecting the structural comprehensive performance as well as their optimization trends. The proposed metamaterial thin plate achieves a maximum average vibration attenuation of up to 40 dB within 1000 Hz, and the lowest initial attenuation frequency is as low as 68 Hz. This work demonstrates significant application potential in lightweight structural design, vibration reduction, and elastic wave manipulation, particularly in lightweight vibration reduction scenarios.

High-load structural materials inherently transmit vibrations with high efficiency, leading to a fundamental trade-off between load-bearing capacity and vibration isolation, particularly in practical engineering environments such as large-scale machinery applications. This trade-off is especially evident in porous structures represented by triply periodic minimal surface (TPMS) lattices. These structures offer high specific strength and lightweight load-bearing capacity yet lack adequate low-frequency vibration isolation, with their mechanical and damping performances strongly volume fraction-dependent. Bioinspired by cat paw pads, we proposed a novel strategy integrating topological discretization with a viscoelastic interpenetrating phase to address this challenge. Results show that the TPMS-Gyroid lattices with 1–8 interlacing cells were fabricated via laser powder bed fusion at a constant volume fraction and infiltrated with silicone rubber. Multi-path load transfer enables uniform stress distribution, silicone rubber constrains strut deformation, enhances energy absorption, and extends fatigue life through interfacial friction and viscoelastic dissipation. Shaker tests confirm improved low-frequency vibration level difference (VLD) via lowered natural frequency and enhanced damping ratio. Experimental validation in a ship propulsion shaft system demonstrates the hybrid metamaterial achieves 39 dB VLD at 55 Hz and up to 1201% higher vibration attenuation than solid bearings under realistic axial displacements, while maintaining excellent load-bearing performance. These results provide a scalable design approach for high-load, low-frequency vibration isolation in large-scale machinery, automated industry, and electronic devices.

Significant vibration coupling exists between the propulsion shaft system and the shell, as well as between the inner and outer shells of underwater vehicles. An in-depth study of these coupling mechanisms helps reveal the vibro-acoustic response characteristics of the stern section of underwater vehicles. This article establishes the dynamic equations for the inner and outer shells based on Flugge shell theory. Then, the dynamic model of the double-layer shell is developed by the displacement continuity conditions and internal force balance conditions between the intercostal structure and shells. Subsequently, the annular flow field between the inner and outer shells is solved using the Helmholtz wave equation and the displacement continuity conditions at the shell surface. The dynamics model of the propulsion shaft system is established using the Euler-Bernoulli beam theory. The bearings are simplified as a stiffness-damping system, serving as the connecting structure between the shaft and the double-layer shell. By balancing the bearing forces between the shaft and the shell, the dynamic model of the propulsion shaft system - double-layer shell coupling system is finally established. The impact of variations in bearing parameters and the connection form between the double-layer shells on the vibro-acoustic characteristic of the propulsion shaft - double-layer shell coupling system is discussed in detail. This study provides theoretical support for vibration and noise reduction in the stern of underwater vehicles.

The propeller generates longitudinal pulsating forces in a non-uniform flow, transmitting through shaft-shell system and causing underwater acoustic radiation. The thrust bearing, as a key coupling component, exhibits variable stiffness and damping, affecting vibro-acoustic response of system. A numerical model based on fluid lubrication theory is developed to determine dynamic characteristics of thrust bearing oil film stiffness and damping. Analytical models for shell and shaft are created using Fl & uuml;gge's theory and Euler beam theory. The combined stiffness from oil film and bearing seat acts as a coupling parameter between shaft and shell, forming a semi-analytical dynamic model. This study examines the impact of thrust bearing dynamic characteristics on shaft-shell system's vibro-acoustic properties. Results show that at high rotational speeds, the increase in vibration and acoustic radiation is primarily due to growing excitation forces. Under constant excitation forces, higher rotational speeds enhance the lubrication performance of the thrust bearing, reducing vibrational energy transmission between shaft and shell. Increasing radius and circumferential width of bearing pads can enhance the lubrication performance of the thrust bearing and reduce vibro-acoustic radiation. Sensitivity analysis reveals that compared to circumferential width, the radius of bearing pads plays a more dominant role in determining both lubrication and vibro-acoustic performance. Increasing number of bearing pads may negatively impact lubrication of the thrust bearing, while it is beneficial for reducing vibration and noise.

Locally resonant (LR) elastic metamaterials, characterized by unique bandgap (BG) properties, provide an effective solution for controlling low-frequency noise and vibrations. Inspired by kirigami design principles, this study proposes a simple X-shaped elastic metamaterial plate (XSEMP) containing an LR metastructure. By integrating Bloch’s theorem with the finite element method, the band structure of the X-shaped unit cell is analyzed and the vibration attenuation performance is evaluated along with the BG simulation results using transmission loss spectra. A comprehensive BG analysis method is developed by introducing vibration modes, iso-frequency curves, group velocity, phase velocity, and isolation properties. This approach provides theoretical insights into the underlying mechanisms and relationships that control the opening and closing of BG, wave propagation, and vibration attenuation. Genetic algorithms are combined with BG topology optimization, using an improved adaptive genetic algorithm for on-demand, reverse-engineered adjustment of optimal BG structures. The results demonstrate that the XSEMP has excellent complete ultra-wide BG in the low-frequency subwavelength range and attenuation properties of multi-band elastic waves. This research provides new perspectives for achieving vibration and noise reduction in low-frequency and multiple wide bands, simplifying the design of elastic metamaterials, and optimizing the topology of BG.

Lattice metamaterials have been proven to be effective for vibration reduction and isolation, but they do not perform well in the low-frequency bands. In this work, inspired by traditional Chinese Taoist concept, multiple IWP-type TPMS lattices are interlaced with each other to achieve low-frequency vibration isolation. The normal IWP lattice (NIL), double interlacing IWP lattice (DIIL), and quadruple interlacing IWP lattice (QIIL) are designed and prepared by the laser powder bed fusion (LPBF) technique. The frequency response and vibration isolation performance of the TPMS lattice metamaterials are analyzed through the dynamic vibration testing and shaft system vibration testing, respectively. The results reveal that the multicell interlacing IWP lattice metamaterials have better low-frequency vibration isolation performance than body centered cubic (BCC) and normal IWP lattices. With the increase of the interlacing-cell number, IWP lattice metamaterials have a better vibration isolation effect in the low-frequency band. Notably, the 316L QIIL metamaterials have superior vibration isolation performance with the maximum vibration level difference of 47.44dB. This study offers a new perspective for the application of lattice metamaterials in low-frequency vibration reduction and isolation.

The thrust bearing is a critical component for power transmission and vibration coupling between the propulsion shafting and the shell of the underwater vehicle. Identifying thrust bearing parameters is crucial for studying the vibration and diagnosing bearing faults of the underwater vehicle. In this study, key information was extracted from the frequency response function (FRF) of the shafting-shell coupling system, and then the artificial neural network (ANN) was used to predict the stiffness and damping of the thrust bearing. The dataset used to train the ANN came from the analytical dynamic model of the shafting-shell system. This analytical approach offers high computational efficiency, making it feasible to generate a substantial amount of training data within a reasonable timeframe. In the analytical dynamic model, the shell was modeled using the Flügge theory, while the shafting system was modeled using the Euler-Bernoulli beam theory. The bearings were simplified as a spring-damping system to represent the connection between the shafting system and the shell. This study employed two ANN algorithms: Backpropagation Neural Network (BP) and Genetic Algorithm-optimized Backpropagation Neural Network (GABP). The results indicate that both BP and GABP effectively predict the stiffness and damping of thrust bearings. Moreover, GABP demonstrates more stable prediction results with smaller prediction errors. The proposed method for predicting thrust bearing parameters leverages features from the FRF to train the ANN, which provides good robustness, maintaining effective results even when the signal-to-noise ratio of the FRF is reduced. The thrust bearing parameter prediction model was validated through experiment, confirming the effectiveness of using ANNs to predict bearing parameters in shafting-shell coupling systems from FRF. This study realizes efficient prediction of bearing parameters, providing a reference for vibration reduction, operational state monitoring, and fault diagnosis of underwater vehicles.

Vibration control is of great importance for the shipbuilding industry. Vibrations not only affect the comfort of the passengers, but also accelerate the wear and even fracture of mechanical components. Aiming at decreasing the transverse vibration of marine propulsion shaft, a multi-channel active control scheme based on electromagnetic actuators on the bearing housing is proposed. The configurations of error sensors in the multi-channel active control system are carefully optimized using an intelligent optimization algorithm to control the overall vibration of shaft with two active control channels. Numerical results show that the multi-channel active control scheme proposed and the intelligent optimization algorithm adopted are effective in the vibration reduction of the propulsion shaft in terms of mean square accelerations. In addition, experiments of the optimized active control scheme are conducted and results are in consistent with those of numerical simulations. The study provides a solution to the overall vibration suppression of the ship shaft system.

Active control is effective in reducing the low-frequency vibration and acoustic radiation of the stern system of an underwater vehicle. This paper theoretically investigates the reduction of vibration and far-field radiation noise in the stern system of an underwater vehicle arising from propeller bearing forces and surface force excitations. Based on the Flügge theory and Euler–Bernoulli theory, an analytical dynamic model of the shaft-shell system is established. The effectiveness of the analytical model is verified through finite element and boundary element methods. The impact of actuator placement, error signal selection, and control strategies on the effectiveness of active control is discussed. A combined active control scheme for the shaft-shell system, involving electromagnetic actuators installed on both the shaft and the shell, is proposed. This scheme effectively controls shaft vibration, shell vibration, and far-field acoustic radiation simultaneously. The theoretical model established in this paper can be used as a reference for low-frequency vibration control of an underwater vehicle.

Because of its high efficiency, high torque, relatively low voltage and other advantages, the dual three-phase permanent magnet synchronous motor has been fully used in the pod propeller, and the control of its vibration and noise level is particularly important. In this study, we develop a mathematical model for the dual-three-phase permanent magnet synchronous motor (PMSM) by examining its operational principles. Subsequently, we employ electromagnetic simulations and modal superposition techniques to evaluate the electromagnetic force and associated noise characteristics of the motor. Finally, the noise size under various speed is analyzed, and the relationship between the noise value and the motor speed is obtained. The model can then be used to optimize the noise generated by the motor.

During the navigation of underwater vehicles, the numerous mechanical components inside the shell inevitably generate vibrational noise. Accurately identifying the primary excitation sources is of great significance for vibration and noise reduction. Direct noise source separation faces challenges such as the limited internal space in the shell, making it difficult to arrange excitation equipment, severe coupling between transmission paths during equipment operation, and complicated testing procedures. By using the reciprocity method, which measures the response of various mechanical components to an external sound source, these difficulties can be circumvented. This study employs the reciprocity method to analyze the contribution of various mechanical components inside an underwater vehicle to underwater acoustic radiation. First, a comparison between the frequency response functions from direct and reciprocal experiments shows that the trends of the frequency response function curves are consistent, with an amplitude error of within 5 dB, verifying the validity of reciprocity. Subsequently, based on the reciprocal frequency response functions, the acoustic radiation contribution analysis of each mechanical component is conducted and compared with the contribution from direct experiments obtained through operational transfer path analysis. The ranking of acoustic radiation contributions identified by both the reciprocal and direct experiments is consistent, with a contribution error of 10% . This study provides a reference for the identification of noise sources of mechanical equipment in underwater vehicles.

The transverse vibration generated during the operation of the ship shaft interferes with the operation of the equipment and accelerates the aging of bearing components. It also intensifies shaft-shell vibration and increases the level of underwater radiated noise of the ship. Aiming to solve the problem of controlling the transverse vibration of the ship propulsion shaft, an active control method for suppressing the transverse vibration of the shaft is proposed by balancing the control error and convergence speed of the FxLMS algorithm. The method's effectiveness is demonstrated through numerical simulations of active vibration control and shaft bench tests. The experimental results show that the control using the improved algorithm can improve the noise reduction effect of each main characteristic spectral line by more than 4 dB.