# Vibration Energy Harvester Based on Bilateral Periodic One-Dimensional Acoustic Black Hole
## 1 Introduction  
Vibrations can be seen anywhere in industrial production and the surrounding circumstances, especially in structures such as beams or rods in civil engineering and mechanical engineering [1; 2; 3]. This kind of redundant vibration is usually harmful and severely affects reliability and accuracy in various mechanical and precision equipment [4; 5]. However, the health status of the mechanical equipment and engineering structures can be monitored by wireless sensor network (WSN) nodes in real time. Traditional WSN [6] nodes are powered by batteries, which have a limited lifetime and are hard to maintain, especially in harsh environments and remote areas. Therefore, it is extremely important to develop a novel power supply method that can replace batteries with a long lifetime and is easy to maintain. Harvesting energy from the vibrations in the surrounding environment where the WSN nodes are deployed, which can be converted to electrical energy, should be a possible solution. The device that can harvest vibration energy and convert it to electrical energy is a vibration energy harvester (VEH). VEHs can be divided into piezoelectric, electromagnetic and electrostatic types according to the operation principle. The piezoelectric VEH has wide employment through its simple structure and high electromechanical transfer coefficient [7]. A cantilever is used as the primary structure of a traditional piezoelectric VEH with a narrow operation bandwidth and low harvesting efficiency. The nonlinear effect can be used to improve the performance of traditional VEHs. Nonlinear structures are widely used due to their simple structure, which can be integrated into the cantilever beam in a VEH. As a nonlinear structure, the ABHs have wide employment in the field of vibrational reduction, noise reduction and energy harvesting due to the unique energy focus effect. ABHs have structures with geometrical or material parameters gradually decreasing t in thin-walled components such as beams and benches, which can focus the elastic wave [8]. [PERSON] et al. [9; 10; 11] proposed several kinds ofone-dimensional double-leaf ABH beams with nested damping units, unit periodic arrays and spatial V-shaped bending. The low-frequency band gap and vibration characteristics of the structure were analyzed. The application of an ABH structure in energy harvesting has gained a lot of attention in recent years. [PERSON] [12] uses the Lagrange equation to derive the combined equation of the bending vibration of the ABH beam with the piezoelectric layer. The influence of the parameters of the ABH and piezoelectric layer on energy harvesting efficiency is analyzed. [PERSON] et al. [13] established an electromechanical coupling model of an ABH cone structure with a surface-mounted piezoelectric transducer and analyzed the dynamic response with numerical simulation. Simulation results show that the response of the system is better than the traditional structure. [PERSON] et al. [14] proposed an energy harvester integrated with a high-intensity ABH and validated it through experimental tests. In addition, the characteristic that acoustic black holes can gather energy is also applicable to vibration suppression. [PERSON] et al. [15] proposed a new solution to embed 2D ABHs on the support plate to suppress the transmission of compressor vibration to the refrigerator body. [PERSON] et al. [16] focus on the mid- and low-frequency performance of plates embedded with the array of an ABH for energy focalization and vibration and noise suppression. [PERSON] et al. [17] proposed a type of metamaterial plate enabling in-plane ultra-wide vibration isolation in engineering equipment development and experiments show that the effective attenuation ability is compared with the traditional hexagonal lattice. A piezoelectric VEH with a bilateral periodic 1D ABH is proposed in this paper.