# A Piezoelectric Energy Harvester with Bending-Torsion Vibration in Low-Speed Water
## 1 Introduction  
The demand for intermittent low-power, wireless, and small electronic devices is growing. More and more scholars have focused on energy harvesting from vibration since the electric energy can be converted from vibration using piezoelectric materials [1]. [PERSON] et al. [2] suggested that a piezoelectric harvester with a non-resonant structure was the best choice for harvesting energy from low frequency ambient vibration. There are many investigations of piezoelectric harvester with respect to the modeling [3, 4], structures [5, 6] and piezoelectric materials [7, 8]. However, studies are mainly focused on the numerical analysis and experiments using harmonic base excitation. Some scholars began to study a piezoelectric harvester by utilizing ambient vibrations. For example, [PERSON] et al. [9] studied a piezoelectric energy harvester which could harvest energy via the wind. [PERSON] et al. [10] investigated a self-excited fluidic energy harvester, which was tested in a wind tunnel and 0.1 mW of electrical power was produced. [PERSON] et al. [11] researched the phenomena of piezoelectric energy harvesting from freely oscillating cylinders undergoing vortex-induced vibration (VIV). Linear and nonlinear models were analyzed and it was found that the load resistance influences the onset of the synchronization region and the harvesters' characteristics. Energy harvesting by VIV has attracted considerable interest from researchers. The main research aspects are prototype design and fabrication [12, 13], modeling, numerical and experimental analysis of the harvesters [14, 15, 16, 17]. As for the modeling of VIV-based energy harvesters, research on lift fluctuation and vortex interactions is necessary. [PERSON] et al. [18, 19, 20] modeled the lift fluctuation with the existing mathematical representations [21, 22, 23]. The model was applied to analyze the VIV of a cylinder linearlyand nonlinearly. This was proven to be consistent with the practical situation by results of simulation and experiment. [PERSON] et al. [24] investigated the fundamental mechanisms of vortex interactions with flexible structures, which were critical to fluidic electrical energy harvesting. A review of recent studies in the field of energy harvesting from aeroelastic vibrations was reported by [PERSON] [25]. Future recommendations in the field were discussed, including mathematical modeling, realistic loadings and small-sized power conditioning circuit optimization, and prototype fabrication of energy harvesters. Hence, scholars are going to continue to work on the above aspects. The low-velocity water flow that can provide a low frequency vibration has been widely reported on. [PERSON] et al. and [PERSON] et al. [26; 27] researched an energy harvesting eel that utilized piezoelectric polymers to convert the flow energy in the oceans and rivers into electrical energy. [PERSON] et al. [28; 29] studied an upright cylinder and a bicylinder vortex-induced piezoelectric energy harvester which harvest energy from water; the maximum output power of these was 84.49 \(\upmu\)W and 21.86 \(\upmu\)W, respectively. [PERSON] et al. [30] researched the phenomena of piezoelectric energy harvesting using experiments with two tandem cylinders undergoing VIV in water, and the output power of 533 \(\upmu\)W was obtained by the downstream harvester in specific conditions. However, the energy-harvesting ability of their single harvester was slightly weak. Hence, harvesters with high-efficiency in water have become an area of increasing research. Therefore, this paper presents several piezoelectric energy harvesters with vortex-induced bending-torsion vibration. The piezoelectric beam undergoes bending-torsion with a tip eccentric cylinder, which creates a mass eccentric distance between its center of mass and the force target, and results in a coupling between the bending and torsion vibrations. Hence, there is a big effect on the harvesters' natural frequencies and mode shapes due to the bending-torsion coupling.