## 1 Introduction  
Energy harvesting from ambient vibration is considered a promising renewable approach for generating electricity. Different transduction mechanisms have been presented, including electrostatic [1], electromagnetic [2; 3; 4; 5], and piezoelectric [6; 7; 8; 9] transduction. The latter transduction theory has received the most attention. Simultaneously, flow-induced vibration exists widely in nature and contains vast amounts of energy, such as flapping waterweeds in flowing water, swing kelp in the ebb or flow of tides, and undulation of pipes and cables in oceans. When the piezoelectric harvester is placed into flowing water, the vortices shed from the harvester, and then reactivate the harvester, making it vibrate. Due to the piezoelectric effect, the piezoelectric harvester is supposed to convert the vibration energy into electricity. [PERSON] _et al_. [10] first presented an eel-shaped piezoelectric energy harvester with five side-by-side flexible beams, which vibrated mechanically in the vortex street. A 10 \(\upmu\)W output power was achieved at a water velocity of 1 m/s. Subsequently, many researchers focused on piezoelectric energy harvesting utilizing flow-induced vibration. The flow-induced vibration includes flutter-induced vibration (FIV) [11; 12; 13; 14] and vortex-induced vibration (VIV) [15; 16; 17]. As for the FIV, [PERSON] _et al_. [18] investigated a macro fiber composite piezoelectric energy harvester in the water vortex, and 1.32 \(\upmu\)W power was generated at a water velocity of 0.5 m/s. [PERSON] _et al_. [19] studied a piezoelectric beam induced by the vortex shedding from an upstream cylinder, and 200 \(\upmu\)W and 3 mW of power were respectively generated at air velocities of 3 m/s and 5 m/s. [PERSON] _et al_. [20; 21] studied a thin polyvinylidene dil fluoride cantilever beam, and the maximum output power was obtained when the natural frequency of the energy harvester was equal to the vortex shedding frequency. Under the airflow flutter excitation, the airfoil-based piezoelectric energy harvesters were mathematically and experimentally investigated, and it was pointed out that the airfoil-based energy harvester should be an effective way of converting wind energy into electricity [22; 23; 24; 25; 26; 27]. Furthermore, with different cross-section geometries (including square, D-shaped, and triangular sections), some galloping-based piezoelectric energy harvesters were presented to increase the output power [28; 29; 30; 31; 32; 33; 34]. Stimulated by the VIV, some vortex-induced piezoelectric energy harvesters were studied and reported [35; 36; 37; 38]. [PERSON] _et al_. [39] numerically studied a vortex-induced piezoelectric energy harvester which consisted of a cylinder and two piezoelectric beams. The numerical results showed that more power was obtained with a larger cylinder diameter. [PERSON] _et al_. [40] studied a pipeline-shaped vortex-induced piezoelectric energy harvester, and 1 mW was generated at an air velocity of 5 m/s when the cylinder was 40 cm in length and 1 cm in diameter. [PERSON] _et al_. [41] numerically investigated a piezoelectric energy harvester stimulated by means of both VIV and based excitations, and it was found that more power was obtained compared with the VIV alone. Generally, more energy harvesters generate more power. However, the dynamic response of vortex-induced piezoelectric energy harvesting systems with more cylinders would be complex because of the interacting effects. Taking two cylinders as an example, [PERSON] _et al_. [42] studied two vertical piezoelectric energy harvesters arranged in a tandem pattern in the airflow. Both of the harvesters were individually equipped with a circular cylinder and a square section cylinder. It was found that the response of the harvester in the downstream was significantly affected by wake effects of the upstream harvester. This was also apparent in two square-section cylinder piezoelectric harvesters arranged in atandem pattern.