Vibration and noise pollution is one of the main pollution in modern society. In order to obtain good vibration damping effect, more effective phononic crystals should be designed. Based on the theory of elastic wave propagation in solids, three types of phononic crystals are designed in this paper using tungsten blocks embedded in a rubber matrix, which are cup-shaped phononic crystal, solid cylindrical phononic crystal, and hollow cylindrical phononic crystal. Firstly, the band gap characteristics and vibration losses of the three phononic crystals are analyzed by using the finite element method. Secondly, the physical mechanism of band gap formation is explored by vibration modes. Finally, the cup-shaped phononic crystal was introduced into the core layer of the sandwich plate to form the cup-shaped phononic crystal sandwich plate, and its vibration damping performance was analyzed. The results show that the three phononic crystals can form three band gaps in the range of 0–800 Hz, and the first low-frequency band gap starts at about 140 Hz and is all wider than 200 Hz. It is noteworthy that the average loss of vibration transmission of the three types of phononic crystals is more than 69 dB, which possesses stronger damping capability and wider low- and middle-frequency band gaps than the flat plate type phononic crystals. The vibration direction of the phononic crystal is at an angle of 90° to the wave vector, which prevents the propagation of elastic waves. The phononic crystal embedded in the sandwich panel plate is more in line with the actual demand of vibration damping and obtains good vibration damping effect. The research in this paper can provide more feasibility for phononic crystal damping.

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Aiming at the problem of vibration damping of low, medium and high frequency noise in the engineering field, an effective phononic crystal structure is proposed in this paper. Firstly, the energy band structure and transmission loss curve of the proposed phononic crystal are calculated using the finite element method, and the first ultra-wide band gap in the frequency range of 122.47-4360.2 Hz is obtained, and the average transmission loss within the band gap reaches 350 dB. Next, the eigenmodes of the phononic crystal are analyzed and the corresponding equivalent spring system is developed. Numerical calculations indicate that the phononic crystal proposed in this paper can perform excellent noise and vibration reduction below 5000 Hz, and it is found that the peripheral silicone rubber connecting plate plays a crucial role in the width of the ultra-wide band gap.

Purpose One of the key challenges in the research of phononic crystals is achieving small-size control of large wavelengths, which means obtaining low-frequency band gaps with relatively small lattice dimensions. Previous studies have mostly been unsatisfactory in this regard. To obtain lower starting frequencies and more satisfactory band gap widths, this work presents a novel design for a phononic crystal structure. Design Approach The proposed phononic crystal consists of a silicon rubber connecting plate, an epoxy resin substrate, and tungsten metal cone scatterers. Through finite element method (FEM) calculations and analysis, we have successfully achieved an ultrawide band gap. To delve further into the origin of the ultra-wideband gap in a newly conceived phononic crystal, the vibrational modes of this crystal were carefully studied. Findings This work has successfully achieved an ultrawide band gap with a width ranging from 122.47 to 4360.2 in the case of a lattice constant of a = 8.5 mm. It was found that the low-frequency ultra-wideband gap cannot be obtained without the presence of silicone rubber. Furthermore, an equivalent spring model was developed, and the accuracy of this model was successfully validated through meticulous calculations. At last, It is found that d1, d4, h1, and h3 have the most pronounced effect on the ultrawide bandgap, and the intrinsic reason is the fact that they determine the geometric structure of the silicone rubber connection plate. Research Limitations/implications Due to the chosen research method of finite element analysis, the study results may vary depending on the different mesh discretizations, but this type of error is small and can be ignored. Practical Implications This work provides a new design solution for phononic crystal miniaturization. Originality/value Compared with previous reports, the new phonon crystals designed in this paper have smaller size, lower starting frequency, and wider band gap.

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