Locally resonant phononic crystals are a kind of artificial periodic composite material/structure with an elastic wave band gap that show attractive application potential in low-frequency vibration control. For low-frequency vibration control problems of ship power systems, this paper proposes a phononic crystal board structure, and based on the Bloch theorem of periodic structure, it uses a finite element method to calculate the band structure and the displacement fields corresponding to the characteristic mode and vibration transmission curve of the corresponding finite periodic sandwich plate structure, and the band gap characteristics are studied. The mechanism of band gap formation is mainly attributed to the mode coupling of the phononic crystal plate structure. Numerical results show that the sandwich plate structure has a double periodicity, so it has a multi-stage elastic wave band gap, which can fully inhibit the transmission of flexural waves and isolate the low-frequency flexural vibration. The experimental measurements of flexural vibration transmission spectra were conducted to validate the accuracy and reliability of the numerical calculation method. On this basis, the potential application of the proposed vibration isolation method in a marine power system is discussed. A vibration isolation platform mounted on a steel plate is studied by numerical simulation, which can isolate low-frequency vibration to protect electronic equipment and precision instruments.

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Sandwich Plate Structure Periodically Attached by S-Shaped Oscillators for Low Frequency Ship Vibration Isolation

The dynamics of metastructures, incorporating both conventional and internally coupled resonators, are investigated to enhance vibration suppression capabilities through a novel mathematical framework. A close-form formulation and a transfer function methodology are introduced, integrating control system theory with metastructure analysis, offering new insights into the role of internal coupling. The findings reveal that precise internal coupling, when matched exactly to the stiffness of the resonator, enables the clear formation of secondary bandgaps, significantly influencing the vibration isolation efficacy of the metastructure. Although the study primarily focuses on theoretical and numerical analyses, the implications of adjusting mass distribution on resonators are also explored. This formulation methodology enables the adjustment of bandgap characteristics, underscoring the potential for adaptive control over bandgaps in metastructures. Such capabilities are crucial for tailoring the vibration isolation and energy harvesting functionalities in mechanically resonant systems, especially when applied to demanding heavy-duty applications.

Bandgap Dynamics in Locally Resonant Metastructures: A General Theory of Internal Resonator Coupling

Metamaterials have marked notable advancements in vibration damping and energy harvesting. However, the specific impact of internal coupled resonators, encompassing both linear and nonlinear types, has received limited attention from researchers. This study aims to delve into this underexplored area. Utilizing a distributed parameter model grounded in modal analysis, our research investigates the effects of these coupled resonators on metamaterial functionality. We particularly emphasize the influence of varying the position of attached masses and its consequent impact on the bandgap properties. Through developing theoretical and mathematical models for metastructural beams with internally coupled resonators, our approach facilitates future simulations and analyses. This investigation not only provides pivotal insights for the design and optimization of metamaterials but also underscores the possible potential of manipulating resonator properties to broaden their practical applications.

Exploring internally coupled resonator's dynamics and spatial variability in metamaterials for vibration suppression

Low-Frequency BG Analysis and Structural Optimization of Toroidal Helmholtz Phononic Crystal

This paper proposes a novel protective material that enhances the impact resistance of metaconcrete by integrating rubber aggregates. The study delves into the mesoscopic mechanisms of wave attenuation in this material and the regulation of its performance accordingly. It first explores the effect of various design parameters of engineering aggregates on bandgap formation and then further investigates the influence of material viscoelastic properties on its bandgap width. Mesoscale simulations of spalling tests demonstrate that incorporating rubber aggregates can effectively expand the bandgap range, enhance energy absorption, reduce damage to the mortar matrix, and ultimately improve the impact resistance of metaconcrete. Simulation results in the present study highlight the effectiveness of rubber aggregates in strengthening metaconcrete's impact resistance. 

Mesoscale modelling of metaconcrete containing rubber aggregates towards wave attenuation against impact loadings

Band gap extending of locally resonant phononic crystal with outward hierarchical structure

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Band gap extending of locally resonant phononic crystal with outward hierarchical structure