# Ultra-Wide Bandgap in Two-Dimensional Metamaterial Embedded with Acoustic Black Hole Structures
## 1 Introduction  
Low vibration and low noise quality are important goals and features of modern equipment development. Excessive vibration and noise often affect the equipment and the environment. Isolation of vibration and shock waves is of vital importance for a lot of precision equipment and engineering structures. The concepts of metamaterials and intelligent structures have gained increasing research and provide novel ideas for elastic wave attenuation and vibration suppression [1; 2; 3; 4]. Metamaterials are usually made of conventional materials and composed of periodic arrangements of rationally designed artificial structural units, manipulating and controlling elastic waves in ways that are impossible in conventional materials [5; 6; 7]. As the periodicity of the metamaterial or the local resonance unit is comparable to the wavelength of elastic waves, the bandgaps due to the Bragg Scattering mechanism and Local Resonance mechanism arise [8; 9; 10]. The concept of metamaterials provides novel ideas and methods to the research and applications in wave guiding [11], filtering [12], cloaking [13; 14], bandgaps [15; 16; 17; 18], and energy harvesting [19]. Moreover, this fundamental property offers a variety of promising applications in the isolation of vibration and shock waves for a lot of precision equipment and engineering structures [20]. [PERSON] et al. provided a type of spiral phononic crystal for the low-frequency isolation on a ship [21]. [PERSON] et al. reported a type of tailored Mechanical metamaterial with programmable quasi-zero-stiffness features for full-band vibration isolation [22]. [PERSON] et al. proposed a kind of mechanical metamaterials, which can circulate the energy between the metamaterial and the energy source, without passing energy to the payload [14]. Very recently, acoustic black holes (ABHs) have been used as micro-structures for constructing metamaterials for wave control and vibration isolation [23; 24; 25; 26; 27].  
Those reports have obtained beneficial results for the application of metamaterials in the field of vibration isolation. But there are still few reports about the vibration isolation of precise instruments and electronic devices using metamaterials. For example, Figure 1 shows the schematic diagram of the battery pack. Some models have battery packs located at the bottom of the vehicle. Different from traditional fuel vehicles, electric vehicles focus more on the design of the anti-shock systems and the attenuation ability of shock waves, to ensure that the internal battery is not damaged. Figure 1b illustrates one type of battery frame structure. Although these structures have periodicity, their designs don't consider vibration isolation and elastic wave attenuation requirements. [PERSON] and [PERSON] reported a class of hierarchically architected honeycombs in which structural hierarchy can be exploited to achieve prominent wave attenuation and load-carrying capabilities [28]. However, the narrow bandgap can't meet the requirements.  
In this paper, we propose a design of Metamaterial that enable simultaneous vibration. Specifically, the ABH structures are introduced to each cell wall of a conventional hexagonal lattice, which results in the reduction of local stiffness in the cell wall and the local mass in the hexagonal corner. Based on the finite element method (FEM), analyses are performed in terms of the bandgaps and the local eigenstates. Experiments on the finite periodic structure are carried out to validate the numerical results.