## 1 Introduction  
The goal of structural health monitoring (SHM) is to improve the safety, reliability, and/or ownership costs of engineering systems by autonomously monitoring their conditions and predicting incipient damages [1, 2]. Most SHM systems are wired in a wide area or in a harsh environment, resulting in both economical and practical limitations. Owing to the development of MEMS technologies, low power consumption microsensors are designed to embed into engineering structures, and then condition-related signals can be sampled and transmitted wirelessly. Thus, embedded wireless sensor network (WSN) provides effective solutions for SHM [3]. Currently, however, a major concern on embedded WSN is how to provide long-term sources of power [4]. Nowadays, the most promising solution for extending the useful life of embedded WSN is to harvest environmental energy for generating electrical energy, which is commonly called energy harvesting [5]. As one of the promising energy harvesting technologies, piezoelectric vibration energy harvesting (PVEH) has been widely studied to realize self-powered WSNs due to their large energy density and ease of implementation [4, 5, 6, 7, 8]. In most studies, piezoelectric cantilever beams with a proof mass are used as the medium. As for SHM systems, however, a cantilever-like PVEH device has two main drawbacks. The first one is that it needs extra space to hold a bulky proof mass and clamping part. The second one is that it is difficult to effectively harvest low-frequency vibrations due to the length limitation. To cope with these drawbacks, piezoelectric patch-based vibration energy harvesters have been proposed to convert the vibration energy of host structures into electrical energy [9; 10; 11]. Compared with cantilever-like ones, patch-like PVEH devices can be easily integrated into their host structures and are especially feasible for thin structures used in the fields of aerospace, automotive, and marine applications. The key is how to effectively control vibration propagation. During the past two decades, artificial materials and structures with periodic modulations of physical properties have attracted significant attention, especially bandgaps, which are defined as those frequency bands where waves are completely blocked [12]. In particular, bandgaps just meet the challenges of low-frequency and broadband vibration energy harvesting in SHM systems, and artificial material with bandgaps is often called bandgap material. According to the generation mechanisms of bandgaps, periodic structural configurations can be used to design phononic crystals or metamaterials for energy harvesting. [PERSON] et al. investigated one-dimension phononic piezoelectric cantilever beams to widen the resonant bandwidth of a harvester [13]. [PERSON] et al. first used a phononic crystal to harvest acoustic energy [14]. However, the lattice constant of phononic crystal is on the order of wavelength so that its length scale is often too large for low-frequency bandgaps. [PERSON] et al. firstly proposed the concept of acoustic metamaterial for solving the length-scale problem of bandgap materials [15]. Due to the local resonant behaviors of these auxiliary oscillators, bandgaps can be generated in a low-frequency regime. Therefore, metamaterial-like structures provide an effective way for harvesting structural vibrations, which are also called metastructures such as metasurfaces. [PERSON] et al. presented analytical and numerical investigations on a one-dimensional locally resonant piezoelectric metastructure with segmented electrodes under transverse vibrations [16]. [PERSON] et al. proposed to harvest energy from vortex-induced vibration by using metasurface [17]. [PERSON] et al. studied numerically and experimentally locally resonant bandgaps in a homogeneous piezoelectric plate covered by a 1D periodic array of thin electrodes connected to inductive shunts [18]. [PERSON] et al.