# Fluid Flow-Based Vibration Energy Harvesters: A Critical Review of State-of-the-Art Technologies
## 7 Enhancement Methods to Optimize and Increase the Efficiency of FBEHs
### Nonlinear FBEHs
#### 7.1.2 Nonlinear Galloping PE-FBEHs  
In the case of galloping energy harvesters, many researchers have focused on the nonlinear techniques for a wider range of wind speeds and to reduce the critical speed for galloping to occur. [PERSON] et al. [160] studied a two-degree-of-freedom galloping energy harvester in which two magnets generated a nonlinear spring stiffness effect. In comparison to a conventional energy harvester, the harvester successfully extracted energy from the reduced wind speed and produced enhanced power. [PERSON] et al. [161] used a nonlinear restoring force. In their research work, the magnetic force was modeled as a nonlinear spring with a quadratic potential energy function that, due to its bistable property, can exhibit spring softening and hardening effects. Similarly, another bistable EH was developed by [PERSON] et al. [162] by utilizing Y-shaped curved wings as illustrated in Figure 12d. The results conclude that coherent large vibration amplitudes can be attained across various airflow velocity ranges. [PERSON] et al. [163] suggested an effective configuration for the resistor, inductor and supercapacitor to identify the optimized RLC circuit that concurrently attributes the best electrical damping and tolerable inductance for improved electrical impedance in galloping energy harvesting systems. Through theoretical predictions and wind tunnel tests, by adding the supercapacitor to the galloping system at low-velocity wind, the harvester's power generation increased by 450%. However, there is a need to reduce the cut-in wind speed for low-frequency applications. [PERSON] et al. [164] developed a double-beam piezo-magneto-elastic energy harvester for which the critical wind speed to activate the galloping vibration was decreased by 41.9%. The prototype consisted of two piezoelectric beams, both supported by a prismatic bluff body. To create a bistable nonlinearity, the tip magnets were positioned so that the magnets repelled one another. This significantly dropped the critical wind speed. A PE-FBEH based on tristable galloping was fabricated [165] by adding a nonlinear magnetic force to the conventional galloping-based energy harvester. According to numerical findings, at a wind speed of 7 m/s, a maximum output power of 0.73 mW was reported. Many researchers have developed theoretical models for galloping-based energy harvesters and validated them for optimization in realistic environments. A multi-field nonlinear model for environment-coupled galloping energy harvesting was established in [89]. The wind tunnel was divided into sections for power generation, flow stabilization, flow contraction, harvester testing and flow diffusion. Through the contraction region, the incoming airflow's velocity was increased to the trial speed of up to 30 m/s. The flow state gradually changed from laminar flow to turbulence as the wind speed increased. Three cross-sectional shapes of the bluff bodies, a semicircle, a triangle and a trapezoid were tested; all had the same height, width and mass and were positioned windward. The trapezoidal bluff body produced superior aerodynamic and energy harvesting capabilities. Withthe environment's adaptable load resistance, the cut-in galloping speed of the harvester was reduced to lower than 1 m/s for the galloping to occur. A PE-FBEH with a sliding bluff body introducing nonlinear spring configuration was proposed by [PERSON] et al. [166]. Figure 12c illustrates that the bluff body was made to move in the axial direction while being restrained by an elastic beam, and a set of springs was attached in between. The imbalance between the drag, centrifugal force, spring and friction forces governed the motion of the bluff body. The effect of the sliding bluff body (distance traveled = effective beam length) on the performance of the harvester was investigated in terms of critical wind velocity, transverse displacement, average power and power density.