Flexible structures, like slender rods, beams and pipelines suffer from dense modal distributions, making broadband vibration suppression highly challenging. Metamaterial bandgaps provide a viable solution, though traditional methods-using low-frequency locally resonant bandgap and high-frequency Bragg bandgap-are either narrowband or demand impractical mass ratios. This study introduces a reverse strategy using a slender pipeline as a flexible model. We synergistically couple a low-frequency Quasi-Bragg bandgap (0-129 Hz, zero-frequency bandgap) from periodic clamps with a high-frequency locally resonant bandgap using lightweight resonators (similar to 10% mass ratio). We analyze the origin of each bandgap and the edge frequencies, through waves, vibration, and mode shapes, then examine the influence of system parameters to analyze the modulation patterns of the bandgaps to widen the bandgaps. Specifically, we find that nonperiodic clamps can broaden the low-frequency bandwidth, and further superposing Bragg bandgap and locally resonant bandgap can broaden the desired high-frequency bandwidth. Experiments considering different additional resonators, lattice constant, bandgap coupling, and nonperiodic supports are established to validate the theory. By combining different effects in experiment, we achieve substantial (20-60 dB) and nearly full-band (0-800 Hz) vibration reduction. This work establishes a robust framework for designing flexible metamaterials, offering a highly effective vibration control strategy for critical infrastructure.

Constrained layer damping (CLD) is widely used for structural vibration attenuation; however, its effectiveness in the low-frequency range remains limited. To address this issue, an acoustic black hole (ABH)-profiled constrained layer damping (ABH-CLD) configuration is proposed, in which the damping layer is designed with ABH profiles to enhance low-frequency vibration attenuation. Finite element simulations of beam structures demonstrate that, compared with uniform CLD, the proposed ABH-CLD configuration reduces the first two resonance peak levels by 3.6 dB and 3.7 dB, respectively. Further investigations on plate structures confirm that ABH-CLD can achieve more pronounced attenuation of low-order resonant responses in two-dimensional configurations, with reductions of 3.5 dB and 1.7 dB in the first two resonance peak levels, respectively. The enhanced low-frequency performance is attributed to ABH-induced flexural-wave energy localization and increased viscoelastic shear dissipation in the damping layer, enabling more effective energy dissipation while maintaining comparable overall broadband attenuation performance. In addition, a differential evolution method is employed to optimize the structural and material parameters to improve damping and vibration attenuation.

This study focuses on the linear spectral vibration and multi-modal vibration mitigation of pipeline systems by using a single multi-stable nonlinear energy sink (MNES) which is critical for ship acoustic stealth. Methodologically, the finite element method is employed to construct a dynamic model of the pipeline system, subsequently analyzing an analysis of the system's natural characteristics. Furthermore, an improved MNES configuration is proposed, the working mechanism of which achieves adaptive absorption of the broadband vibrations through potential well transitions, with its integration into the pipeline-MNES coupled system elaborated. To assess the MNES's wideband vibration mitigation capability for the pipeline system, the genetic algorithm (GA) is employed to optimize the vibration-reduction parameters of MNES. Simulations have revealed that under fixed three-frequency base excitation, the suppressions of the MNES can reach 86.2 %, 81.7 %, and 80.6 % for the vibration transmission rate responses, the rates are 90.5 %, 87.3 %, and 98.9 % for the acceleration responses, the rates stand at 82.4 %, 81.7 %, and 80.5 % for the displacement responses, at 24 Hz, 48 Hz, and 120 Hz. Under sweep three-frequency base excitation, the MNES's vibration suppressions for the vibration transmission rate responses are 82.7 %, 83.1 %, and 80.3 %, 82.4 %, 83.4 %, and 80.2 % for the acceleration responses, and 82.7 %, 83.3 %, and 80.4 % for the displacement responses, at 24 Hz, 48 Hz, and 120 Hz. A set of experiments are conducted to validate the reliability and engineering applicability. The findings are that under fixed three-frequency base excitation, the MNES achieves acceleration response suppressions of 88.3 %, 87.7 %, and 86.2 % at 24 Hz, 48 Hz, and 120 Hz. Under sweep single-frequency base excitation, a three-mode resonant vibration excitation, the suppressions for acceleration responses at 24 Hz, 45 Hz, and 107 Hz are 86.4 %, 84.7 %, and 83.5 %. Test results confirm that MNES exhibits robust broadband vibration damping performance for both linear spectral vibration and multi-modal vibration of pipeline systems.

Modern engineering applications impose stringent demands on structural energy absorption (EA) efficiency and stability. Nevertheless, achieving integrated structural designs that synergize high load-bearing capacity, impact resistance, and lightweight attributes remains a considerable challenge. To address this issue, a bioinspired sinusoidal chiral (BSC) structure, derived from the cortical layer of a feather rachis cross-section, is proposed. The unique configuration of BSC promotes enhanced intercell interactions, which collectively induce global shear deformation under compression. This coordinated deformation mode strengthens the structural negative Poisson's ratio effect, contributing to more stable and efficient energy dissipation. Finite element simulations and quasistatic compression experiments are conducted to evaluate its mechanical performance and EA behavior. Compared with traditional chiral (TC) structures, the BSC exhibits remarkable enhancements, achieving increases of 115.10% in EA, 96.74% in plateau stress, and 10.94% in densification strain under equivalent filling ratios. Additionally, the effects of key geometric parameters-the unit angle, sinusoidal amplitude, and wall thickness-on the EA characteristics were systematically examined. The results demonstrate that increases in both amplitude and wall thickness lead to significant enhancements in load-bearing capacity. Furthermore, the dynamic mechanical response of the BSC structure was evaluated under various impact loading conditions through finite element simulations. This study provides valuable insights for the design of metamaterial structures with superior mechanical and energy-absorbing properties, demonstrating promising potential for engineering applications.

This paper presents a hybrid analytical–optimization framework for identifying the equivalent orthotropic material parameters of stator core and winding assemblies in electrical machines. An analytical cylindrical model is developed based on first-order shear deformation theory and Love's shell theory to establish the relationship between material properties and modal characteristics. The stator core and its components are modeled using equivalent layered cylindrical shells, incorporating structural features such as longitudinal ribs. The Firefly Algorithm is employed to solve the inverse identification problem by minimizing the discrepancy between predicted and measured natural frequencies. The material parameters of epoxy resin and winding insulation are identified, and the corresponding equivalent orthotropic material parameters are derived using composite material theory. The proposed method is validated through both analytical and finite element analyses, showing good agreement with experimental results, with relative errors within 3%. Compared with conventional optimization and data-driven approaches, the proposed framework demonstrates improved accuracy, convergence stability, and computational efficiency. The developed method provides an effective tool for vibration analysis and parameter identification in electromagnetic devices and offers potential for application in structural optimization and noise reduction design.

This work proposes an arc-shaped chiral metamaterial (ACM) for low-frequency underwater sound insulation. The equivalent parameters of the designed arc-shaped chiral lattice (ACL) in the metamaterial are derived and evaluated using homogenization method. It is demonstrated that the arc central angle serves as a key geometric parameter for tuning the ACM’s acoustic and mechanical properties. By strategically adjusting this angle, a continuous reduction in equivalent acoustic impedance can be achieved, thereby significantly enhancing impedance mismatch with water. Numerical results for the transmission loss (TL) demonstrate that the metamaterial, designed according to this principle, exhibits excellent low-frequency broadband performance for underwater sound insulation while maintaining a deep subwavelength thickness. Furthermore, a stiffness recovery mechanism is identified at a specific central angle, enabling the design of pressure-resistant configurations that maintain acoustic functionality under a certain hydrostatic pressure. Experimental measurements agree well with simulations, validating the proposed design methodology for developing high-performance underwater sound insulation metamaterials. The insights from this work offer a practical pathway and may aid in the future development of efficient, lightweight underwater sound-insulating metamaterials.

Low-frequency noise control in ship seawater pipeline systems remains challenging, as mufflers are required to deliver good broadband performance within compact spaces. Inspired by bladder mufflers that exploit the strong impedance mismatch between low-impedance air and water for efficient sound reflection, this work introduces low-impedance arc-shaped metamaterials (ASMs) into conventional expansion-chamber mufflers and proposes a compact waterborne muffler. Based on different integration methods between the ASM and the expansion chamber, three muffler configurations are developed: Model B (circular chamber with annular ASM), Model C (circular chamber with revolved ASM), and Model D (square chamber with planar ASM). The equivalent acoustic parameters of the ASM are calculated and analyzed using homogenization theory. Results demonstrate that increasing the central angle of the arc-shaped beam or adjusting the deflection angle of the metamaterial significantly reduces its equivalent acoustic impedance, thereby enhancing low-frequency noise-reduction performance. Numerical simulations show that, compared with conventional expansion-chamber mufflers, the introduction of low-impedance ASM significantly improves the transmission loss (TL) in the low-frequency range and broadens the effective noise-reduction bandwidth. As a proof of concept, a muffler specimen based on Model B is fabricated and tested in a water-filled circulating pipeline system. The measured TL agrees well with simulations, yielding an average TL of 15.7 dB and an average insertion loss (IL) of 10.9 dB in the 200-2000 Hz band. This work provides a new approach for low-frequency noise control in fluid-filled pipeline systems and holds potential for applications in marine engineering and ocean equipment.

Low-frequency vibrations under strong excitations pose significant challenges for conventional vibration control strategies due to pronounced nonlinear dynamics. This study presents a novel locally resonant metamaterial beam featuring amplitude-dependent nonlinear stiffness coupled with particle-based damping, forming a nonlinear stiffness–nonlinear damping (NSND) system capable of actively regulating energy transfer and dissipation. A comprehensive dynamic model is developed, incorporating nonlinear restoring forces and particle-induced dissipation, to elucidate the intricate coupling between stiffness nonlinearity and nonlinear damping mechanisms. A metamaterial beam comprising periodically arranged NSND units is numerically analyzed to investigate frequency-dependent response characteristics and vibration mitigation performance. The results reveal that nonlinear stiffness induces amplitude-dependent bandgap migration, whereas nonlinear damping broadens the bandgap and enhances energy dissipation, thereby achieving effective suppression of vibrations both within and outside the bandgap. Furthermore, a physical prototype is fabricated and experimentally evaluated under varying excitation amplitudes and particle filling ratios, confirming the predicted dynamic behavior and demonstrating the transition from stiffness-dominated to damping-dominated regimes. These findings offer new insights into the design of nonlinear metamaterials, providing a robust strategy for achieving broadband low-frequency vibration attenuation through the synergistic interplay of controlled energy storage and nonlinear dissipation. From an engineering perspective, the proposed NSND architecture is particularly relevant to bridge cables, rail and vehicle components, marine equipment, and fluid-conveying pipe systems in which low-frequency vibrations vary with operating load and excitation amplitude.

Abstract To address the problems of high computational cost, poor generalization ability, and inadequate physical consistency associated with frequency response prediction and inverse parameter design for multi-degree-of-freedom (MDOF) vibration systems, we propose an intelligent design method integrating physics-informed and data-driven approaches. Taking a 10-degree-of-freedom lumped mass-spring system as the research object, we first construct a forward prediction model based on the one-dimensional Residual Network-Physics-Informed Neural Network (1D-ResNet-PINN), then design an inverse generation model of the Physics-Constrained Conditional Wasserstein Generative Adversarial Network (PC-cWGAN), and finally establish a closed-loop intelligent design framework integrating the aforementioned forward and inverse models to realize intelligent structural design. Experimental results demonstrate that the forward model exhibits remarkable advantages in prediction accuracy and generalization ability, the inverse model enables end-to-end generation from response requirements to structural parameters with a substantial improvement in computational efficiency, and the construction of the closed-loop framework provides effective technical support for the intelligent design of complex vibration systems.

To reduce the computational cost of evaluating the acoustic target strength of large-scale underwater stiffened cylindrical shells, a rapid prediction method based on a deep neural network(DNN) is proposed. First, a two-dimensional axisymmetric finite element method(FEM) is established to calculate the acoustic target strength of underwater stiffened cylindrical shells and generate high-fidelity training samples. Then, a DNN is developed to learn the nonlinear mapping between structural parameters and acoustic target strength. The DNN results are in good agreement with those obtained by the two-dimensional axisymmetric FEM, demonstrating the effectiveness of the proposed DNN method. In addition, the computational time for target strength evaluation is reduced by more than two orders. The effects of structural parameters on the acoustic target strength of the cylindrical shell are also analyzed. The proposed approach provides an efficient tool for the rapid prediction of acoustic target strength of large-scale underwater cylindrical shells and shows promising engineering applications.

This paper studies the vibro-acoustic control (VAC) of cylindrical shells using acoustic metamaterials composed of resonators incorporating nonlinear damping using particle damping technology. A cross-scale theoretical model considering macroscopic resonator dynamics and mesoscopic particle damping effects through an equivalent damping model is developed to analyze bandgap structures and vibration attenuation characteristics. Validated via finite element method and experiment, the nonlinearly damped acoustic metamaterial shell (ND-AMS) achieves a dual-mechanism VAC compared with the acoustic metamaterial shell (AMS) of equal mass. This enhanced performance arises from the dual-mechanism synergy of local resonance and nonlinear damping, where the former preserves low-frequency attenuation while the latter introduces broadband energy dissipation. The contribution of the nonlinear damping mechanism increases with both resonator vibration amplitude and the number of resonators in operation. Leveraging this mechanism, the proposed ND-AMS with a 35% filling ratio achieves a 12.8 dB maximum vibration reduction and 19.4 dB averaged (#1-#3 microphones) sound suppression within the test range of 0.1-4 kHz. Moreover, it exhibits both enhanced suppression under high excitation levels and stable performance across different working conditions. By optimizing the number of resonators, a nonlinearly damped discrete resonator shell (ND-DRS) is proposed, which reduces the added mass ratio by 14.7% while maintaining performance comparable to the ND-AMS. Compared to the bare shell, the ND-DRS achieves 22.5 dB vibration attenuation and 12.9 dB sound radiation suppression within the test range. Due to the stability of the materials used, the structure demonstrates potential for operation under extreme conditions. Compared to related research on AMS structures, it exhibits a clear performance advantage, offering highly valuable insights for engineering applications.

Mechanical metamaterials with tunable bending stiffness are significant for realizing smart adaptable machines or structures composed of beams, shells and plates. However, different from tuning longitudinal stiffness, realizing broad-range, continuous, and in situ (without global shape morphing) tunability of bending properties remains a major challenge. Here, we report a deformation conversion principle for designing meta-beams/plates that offer such extraordinary tunability. The metamaterials incorporate planetary gear assemblies as tension-compression fibers within sandwich beams or plates, effectively transferring the localized tunable longitudinal stiffness of these geared units into the global tunable bending stiffness. This principle enables diverse tunable bending modes, including the static bending deformation, vibrational modal shapes and frequencies, and bending wave bandgaps. Their smoothly tunable properties and mechanisms are demonstrated based on analytical, numerical and experimental methods. This work offers a new pathway for developing structures with adaptively tunable bending properties that are free from the constraints of intrinsic material properties, elucidating innovations and applications of mechanical metamaterials and structures for intelligent systems.

Acoustic black holes (ABHs) exhibit excellent dynamic characteristics; however, their weak load-bearing capacity due to insufficient tip stiffness limits their application in lightweight pressure-resistant structures. In this paper, a reversed semi-re-entrant (RSRE)-ABH metamaterial structure (RSRE-ABH) is proposed. By leveraging the zero Poisson's ratio characteristic and the dynamic advantages of ABHs, it achieves a synergistic design of load-bearing and vibration-noise reduction. The dynamic and static performances of the RSRE-ABH are investigated through numerical simulations and asymptotic homogenization methods. The results indicate that the RSRE-ABH can generate an ABH effect, leading to strong attenuation of horizontally propagating S-waves, and its attenuation effect is validated by experiments. Similarly, for vertically propagating P-waves, the ABH structure exhibits local resonance characteristics due to its tip geometry, making its sound insulation and sound radiation suppression performance significantly better than that of the RSRE structure. In terms of static performance, the introduction of the ABH enhances the transverse support stiffness without affecting the characteristics in the primary load-bearing direction. Meanwhile, the zero Poisson's ratio property of the structure effectively suppresses transverse strain, thereby avoiding excessive stress at the tip of the transversely placed ABH, allowing it to maintain good load-bearing capacity under 5 MPa hydrostatic pressure. Experiments further verify the static characteristics of the structure.

ABSTRACT Actively and smoothly tunable mechanical metamaterials are in high demand for adaptive, variable‐stiffness structures in smart machines. However, existing designs are largely restricted to tunable transverse deformation, reciprocal response, and linear dynamics. Here, we propose a novel gear‐based design paradigm—using Taiji planar gears and planetary gear assemblies as building blocks—that overcomes these limitations by enabling simultaneous control of translational and torsional stiffnesses, shear nonreciprocity, and programmable nonlinear dynamics. Our metamaterials achieve in situ, continuous tuning of shear stiffness by 30–100×, break reciprocity under positive versus negative loads, and allow the nonreciprocity ratio to be tuned by over 100×. Meta‐resonators constructed from these units showcase an application example exhibit broadly tunable transverse and torsional resonant frequencies. Furthermore, we demonstrate that static nonreciprocity serves as a precise control knob for dynamic nonlinearity—a property traditionally fixed and nearly impossible to tune in conventional materials. Analytical models and analyses elucidate the underlying mechanisms and extendable design freedoms. This work bridges the critical gaps in mechanical metamaterials and dynamics, offering a practical pathway to control both linear and nonlinear structural deformations, elastic waves, and vibrations.

The static modulus of natural solids fundamentally scales with the square of elastic wave speed. This intrinsic coupling has long constrained the development of underwater sound-absorbing materials, which demand both high modulus and slow wave propagation for deep-sea applications. This property trade-off causes existing materials to suffer pressure-induced performance degradation. Here, we overcome this fundamental limitation through morphogenesis design, leading to the discovery of an extremal elastic metamaterial. By engineering a tailored distribution of hard and soft modes with weakly coupled isotropic-isochoric eigenmodes, the metamaterial achieves unprecedented decoupling between static modulus and wave speed, delivering a 6.8-fold modulus enhancement relative to the theoretical limit of isotropic materials. Transcending prior designs, a composite integrating this metamaterial with rubber demonstrates pressure-invariant underwater sound absorption, maintaining an average coefficient exceeding 0.9 across a three-octave low-frequency band under extreme pressures up to 4.5 MPa.

This work proposes a compact waterborne muffler by integrating acoustic metamaterials (AMMs) with low acoustic impedance into a conventional expansion chamber. Based on homogenization theory, the equivalent acoustic parameters of the designed metamaterial are calculated and analyzed. It is demonstrated that the metamaterial’s acoustic impedance can be effectively reduced by strategically tuning its structural parameters and principal orientation, and the underlying physical mechanism is revealed. Numerical simulations show that, compared with traditional expansion chamber mufflers, the introduction of low-impedance metamaterials significantly enhances the muffler’s low-frequency transmission loss (TL) and extends its effective bandwidth. As a proof-of-concept, a waterborne muffler embedded with two low-impedance AMM specimens is fabricated and tested in the water-filled circulation pipeline system. The good agreement between measured and simulated results verifies the acoustic performance of the designed muffler. This work may provide new insights into noise control in fluid-filled pipeline systems and has the potential for application in ocean engineering and related industrial fields.

Mechanical vibration and complex loading environment pose serious challenges to the reliability and service life of equipment structures, and new multifunctional material structures with both high load-bearing capacity and low-frequency broadband vibration damping characteristics are urgently needed. In this paper, we propose a vibration- and pressure-resistant integrated three-dimensional mechanical metamaterial beam, which realizes the synergistic regulation of static load-bearing and dynamic vibration-damping performance by integrating the pressure-resistant advantage of negative Poisson's ratio honeycomb core with the bandgap characteristic of local resonance metamaterial. Combined with finite element simulation and experimental verification, the influence of the vibrator arrangement on the bandgap characteristics is systematically investigated. The results show that the metamaterial beams form a broadband low-frequency damping bandgap of 436.3 Hz in the frequency band of 155.6–591.9 Hz when the ratio of the lattice constant to the size of the matrix element cell is 1:3, which is a 30.9

In recent years, the invention of metastructures has greatly promoted the low-frequency sound insulation technique. However, it is still a difficult task to design multifunctional metastructures that possess light weight, high load-bearing property, and good sound insulation performance at broadband low frequencies. To challenge this problem, this study presents a double-panel metastructure comprising two lightweight sandwich plates with lattice truss-core that are separated by an air gap. By perforating the faceplates of the sandwich plates, the double-panel metastructure can realize acoustic resonance without additionally introducing resonators. For efficient calculation and in-depth analysis of the double-panel metastructure, we develop a semi-analytical method by dynamic homogenization of the fluid and solid domains. The effectiveness of the modeling method is verified by comparing it with the vibroacoustic finite element method. The results of numerical examples demonstrate that the double-panel metastructure can exhibit two low-frequency sound insulation peaks. Within a broadband low-frequency range around the two peaks, the sound transmission loss of the double-panel metastructure is much higher than that of traditional double-panel structures and the mass law. Further, the influence of structural parameters is analyzed and an optimization procedure is conducted. Finally, the sound insulation of the metastructure and the load-bearing capacity of the separated sandwich plates are confirmed by comparative experiments.

Elastic metamaterials enable the modulation of low-frequency elastic waves through strategically engineered bandgaps, offering promising applications in vibration control. However, achieving integrated functional designs that combine effective vibration attenuation, impact resistance, and high load-bearing capacity remains a critical challenge. To address this limitation, we propose a novel pre-torsion tubular metamaterial (PTM) capable of generating a low-frequency flexural bandgap (normalized frequency fnd = 0.054-0.073) and a broad compression-torsion coupled bandgap (normalized frequency fnd = 0.04-0.11). The band structures are systematically investigated through the finite element method and theoretical method based on an equivalent discretized model, revealing that the low-frequency bandgaps originate from a torsional inertial amplification mechanism (IAM). The characteristics of the evanescent wave propagation within bandgaps are analyzed through complex band structures, and the underlying bandgap formation mechanism is elucidated from the perspective of wave mode coupling. The wave suppression performance of the PTM is experimentally validated by measuring the steady-state response under vibration excitation, showing that the vibration velocity amplitude within the bandgap is attenuated by up to 97.4 %. Additionally, dropping ball impact tests are also carried out to demonstrate the remarkable impact resistance performance, where the maximum impact peak acceleration is reduced by 63.1 %. The developed PTM exhibits superior vibration suppression and impact resistance capabilities, while its lightweight nature and tunable bandgaps highlight the potential for vibration/shock mitigation in aerospace equipment systems.