# A Flutter-Based Electromagnetic Wind Energy Harvester: Theory and Experiments  
[PERSON]  
1 Microsystem Research Center, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China; [EMAIL_ADDRESS]
2 Key Laboratory of Fundamental Science of Micro/Nano-Device and System Technology, Chongqing University, Chongqing 400044, China
3 Fraunhofer ENAS, Technologie-Campus 3, 09126 Chemnitz, Germany  
4 Correspondence: [EMAIL_ADDRESS] (Z.L. ); [PERSON]DDRESS] (Q.W. ); [EMAIL_ADDRESS] (Z.W.) November 8, 2021 November 8, 202  
frequency is close to the natural frequency of the elastic structure, a resonance phenomenon takes place and the amplitude increases dramatically. [PERSON] et al. [13] compared the output performance of a piezoelectric energy harvester with different orientations of buff body; the results confirm that the vortex-induced aerodynamic force acts on both the buff body and the rear cantilever. Differing from VIV, flutter is a self-excited vibration phenomenon--The aerodynamic forces mainly come from the vibration of the structure itself, which is possible when the total damping is negative. According to the number of vibrational degrees of freedom, flutter can be divided into two forms: single-freedom flutter (also known as galloping) [14; 15; 16] and bend-torsion coupled flutter [17; 18]. Galloping is normally observed in lightweight prismatic structures (square, triangle, D-section, and so on). VIV and galloping may occur simultaneously. [PERSON] et al. [19] investigated the performance of a piezoelectric energy harvester by utilizing buff bodies with a different rectangular section; the results show the enhancement of wind energy harvesting on interaction between VIV and galloping. Bend-torsion coupled flutter usually occurs in plate-like structures, such as membranes, flat plates, and airfoils. [PERSON] et al. [20] proposed the concept of bionic tree, wherein hundreds of leaf-like piezoelectric energy harvesters show prospects for high-power applications. When compared to piezoelectric energy harvesters, electromagnetic energy harvesters offer the advantage of lower internal resistance, which results in a higher current. [PERSON] [21; 22; 23] invented a flutter-based electromagnetic wind energy harvester, known as the wind belt. The energy harvester had an extremely simple structure consisting of three parts: a doubly-clamped membrane, two pieces of magnets, and one or more coils. [PERSON] claimed that the energy harvester--With two dimensions of 12 cm and 1 m--Could be used for the power supply of an island. [PERSON] et al. [24] introduced the aerodynamic forces of the wind belt and designed a power management circuit for the energy harvester. [PERSON] et al. [25] experimentally investigated the effects of axial tension, angle of attack, and position of magnets on critical wind speed, oscillating frequency, and output performance of the energy harvester [PERSON] et al. [26; 27] made a wind belt with a length of 0.5 m and simulated the wind field around buildings; they also suggested the optimal installation location of the energy harvester. However, although a series of experiments have been conducted on the wind belt type energy harvester, an analytical model to systematically analyze its behavior is missing. In this paper, an analytical model for the wind belt type energy harvester is proposed. Modal analysis of the model agrees well with that of the finite element simulation. The results of flutter analysis indicate that flutter at low airflow speed mainly comes from the coupling of the first bending and torsional modes. The calculated critical wind speed was consistent with previous empirical formulae and the experimental results. The influence of the magnets' positions was also investigated. The results suggest that by placing the magnets near the middle of the membrane, the performance of the system could be further improved.