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In order to attenuate the various low-frequency vibrations that may cause structural fatigue and damage, impact human health and affect work efficiency, this paper presents a novel local resonance metamaterial sandwich meta-plate structure containing a cantilever spiral beam-mass resonator, and investigates vibration reduction effects of it within the obtained low-frequency bandgap range. For this purpose, a theoretical model of the low-frequency resonator being composed by a cantilever Archimedean spiral beam and cylindrical mass is established. The natural frequency of it is calculated by solving the Euler-Lagrange equation of the resonator. The accuracy and reliability of the theoretical model are verified through COMSOL simulation. The stress distribution of five types of cantilever spiral beam mass resonators (i.e. Archimedes spiral, triangle spiral, square spiral, pentagon spiral and hexagon spiral) and different cross-sectional shapes (rectangular, square, circular, diamond and triangular) are analyzed. Then, a unit cell model of a sandwich meta-plate with a cantilever Archimedean spiral beam resonator is selected. Hamilton’s principle is used to deduce the bandgap range under infinite periods, and the theoretical solutions are also verified. The parameter optimization of the substrate plate and resonator are also studied. Moreover, the effects of the various structural variables on the bandgap range are systematically explored. Finally, the dynamic responses of the sandwich meta-plate composed of $5\times 8$-unit cells under different excitation frequencies, boundary conditions and structural damping are analyzed.

The bandgap characteristics of periodic double-span beams are analyzed using spectral geometry methods in this paper. The displacement function of the beam structure is represented in a unified form, supplemented by sine series in addition to Fourier cosine series to avoid discontinuities in displacement at the boundary positions. The introduction of artificial spring technology satisfies the strong coupling connection conditions between beams. Combining it with Bloch’s theorem allows the separation of boundary conditions and displacement functions, ensuring the convergence and accuracy of the method. The energy functional of the double-span beam under periodic boundary conditions is established. The bandgap characteristics of the double-span beam can be obtained using the Rayleigh–Ritz method. The bandgap characteristics calculated based on the proposed method are in good agreement with those obtained from the transfer matrix method, and the bandgap frequency range matches well with the vibration attenuation range obtained from the test results. The effectiveness of forced vibration analysis for finite periodic double-span beams is also validated through the finite element method. Additionally, the influence of material properties, geometric parameters and lattice constants on the bandgap characteristics of periodic double-span beams is presented, providing insights into the mechanisms for tuning bandgap characteristics.

This paper presents a comprehensive study and it concludes that the resonance of forest trees with properly aligned conditions precisely working as naturally available locally resonant metamaterials that are equipped with wonderful capability of generating low frequency extremely wide bandgaps in the earthquake frequency range of interest. At the geophysical scale, the propagation of Rayleigh wave in the soft sedimentary soil basin experiences strong wave attenuation when the longitudinal resonant modes of trees are coupled with vertical component of the Rayleigh wave that mimic wave hybridization phenomena. A finite element-based numerical technique is adopted and we considered a total of 10 cases where spacing, height, thickness and mechanical properties of resonant trees are varied to study the Rayleigh wave propagation and attenuation mechanism. The trapping and/or mode conversion of Rayleigh wave by resonant trees is observed as dominant phenomena for wave attenuation. A time history analysis is conducted based on an actual earthquake record to validate the performance and efficiency of the bandgaps. The effects of ground stiffness, resonant tree mechanical and geometric properties on the bandgaps are also discussed. The study explores another peculiar characteristic of the forest trees that controls the propagation of seismic wave to protect a region from earthquake hazards. Our study may motivate the relevant organizations, authorities and global communities on the needs of forestation to reduce the earthquake catastrophe.

Functionally graded material (FGM) beams are widely used in engineering as moving components. Nevertheless, their generated vibrations usually become annoying. To realize multi-broadband vibration reduction of FGM beams, an enhanced multiple dynamic vibration absorber (EMDVA), which utilizes an amplification mechanism, is proposed in this study. The devices are periodically arranged on the FGM beams. The dispersion and vibration transmission characteristics of the structure are investigated using the energy method and nullspace technique. The accuracy of the model is verified using the finite element method. The effects of parameter on its vibration damping performance are also analyzed. Finally, the relationship between the amplification coefficient and the operating performance of the EMDVA is revealed in terms of both the impedance principle and the energy method. The results show that the amplification mechanism can amplify the stiffness, damping, and mass of the MDVA by a factor of square of the amplification coefficient. Therefore, the proposed EMDVA has a wider damping band and stronger attenuation performance compared to the conventional MDVA. This study provides a simple and easy-to-implement solution for multi-band vibration reduction in FGM beams, which is useful for the engineering application of FGM beams in vibration and noise reduction.

Two novel seismic metamaterials models, trophy and apple core, inspired by an ancient Chinese puzzle are proposed in this study. Bandgaps below 15Hz are achieved by exclusively using concrete as the base material in the designs. Vibration modes are investigated to clarify the bandgap formation. Through comparison, we found that under the same volume, the apple core model can provide a lower frequency bandgap than the trophy model. Results from transient simulations and band structures are in good agreement, validating the accuracy of the simulation results. To broaden the bandwidth, the radii of the apple core models are varied and arranged in a gradient pattern. Transient analyses using a Gaussian wave packet and Taiwan’s Chi-Chi earthquake dataset are conducted to verify the effectiveness of the gradient apple core seismic metamaterial.

Train vibrations are the primary concern in environmental engineering and civil engineering. It is significantly imperative to find new methods for reducing and isolating vibrations. The locally resonant metamaterials (LRMs) propose a novel method and concept for reducing train vibration. However, the accurate and quick design structures of LRMs based on vibration characteristics are still an issue. Thus, this study presents a novel inverse design model of three-component locally resonant metamaterial barriers (LRMBs) for vibration reduction based on deep learning. The bandgap characteristics and vibration modes of the LRMB are investigated by using the improved plane wave expansion (IPWE) and finite element method (FEM). Besides, the gradient-combined LRMBs are proposed based on time–frequency features of measured vibration caused by trains and the novel inverse design model, and a two-dimensional finite element model coupling with infinite element boundaries is established to study the reduction efficiency of the gradient-combined LRMBs. And the performances of different LRMBs are fully analyzed in time and frequency domains. The results show that the novel inverse design model can be successfully used to design the LRMB based on vibration features. Moreover, the gradient-combined LRMBs have better isolation performance.