Intended for the vibration and noise control problems faced by many engineering fields, a fresh variety of phononic crystal beam structure was constructed by attaching a one-dimensional periodic multilayer cylinder to a double-layer beam structure. Utilizing the finite element method and the Bloch theorem, the vibration modes of the band structure, the critical point of the band gap and the associated finite structure’s vibration transmission is estimated, and then the band gap characteristics of the structure are comprehensively studied. The results show that reasonable parameter design can achieve vibration and noise control in a certain frequency range. Based on the modal analysis, the mechanism of band gap opening is revealed. By comparing the single-layer beam and double-layer beam with the same parameters, the advantages of the double-layer beam in vibration reduction and noise reduction are shown. The study’s findings offer a fresh concept for ship engineering disciplines including vibration and noise reduction technology.
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.
First, this study proposed a metamaterial beam model with spatially varying interval density. The interval dynamic equation of this model could be established by incorporating the decomposition results of the interval field based on Karhunen–Loeve expansion into the finite element method. An interval perturbation finite element method was developed to evaluate the bounds of the dynamic response interval vector. Then, an interval vibration transmission analysis could be performed, and the frequency range of the safe band gap could be determined. Meanwhile, Monte Carlo simulations and the vertex method are also presented to provide reference solutions. By comparison, it was found that the calculation accuracy of the interval perturbation finite element method was acceptable. The numerical results also showed that the safe band gap range was significantly smaller than that of the deterministic band gap.
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