# 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
#### 7.1.3 Nonlinear Flutter PE-FBEHs
Five vibration forms were observed, including intrawell limit cycle oscillations (LCOs) in the first, second and third wells, and additionally aperiodic responses, and interwell LCOs between the three potential wells. The experiment yielded a peak-to-peak voltage of 28.17 V at 15.5 m/s. Table 6 lists and compares nonlinear energy harvesters based on aerodynamic instabilities, i.e., VIV, galloping and flutter. Nonlinearities are categorized as magnetic nonlinearities, resulting in monostable, bistable and tristable energy harvesters. Nonlinearities are mainly induced to increase the frequency range. Understanding and leveraging magnetic-induced nonlinearities is critical for improving energy harvesting efficiency. Spring structures and cubic spring stiffness are included in the design of energy harvesters, giving rise to nonlinearities. Such designs including nonlinear elements allow for greater flexibility and responsiveness to changing environmental circumstances, hence improving the device's overall performance in these conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Type of FIV**} & \multirow{2}{*}{**Nonlinearity**} & \multicolumn{2}{c}{**Optimum**} & \multicolumn{2}{c}{**Velocity at**} & \multirow{2}{*}{**Output Power**} & \multirow{2}{*}{**References**} \\  & & **Resistance** & & & **Max Power** \\  & & **(k\(\Omega\))** & & **(m/s)** & \\ \hline \multirow{4}{*}{VIV} & Buckled beam & 1000 & 14 & 0.0618 & [PERSON] et al. [152] \\ \cline{2-6}  & Magnetic nonlinearity & 50 & 3.2 & 0.15 & [PERSON] et al. [154] \\ \cline{2-6}  & Magnetic coupling monostable & 500 & 1.6 & 0.21 & [PERSON] et al. [155] \\ \cline{2-6}  & Non-contact PEH & 300 & 40 & 1.438 & [PERSON] et.al [156] \\ \hline \multirow{4}{*}{Galloping} & Magnetic nonlinearity & 600 & 7 & 0.73 & [PERSON] et al. [165] \\ \cline{2-6}  & Nonlinear spring configuration & 504 & 4 & 35 & [PERSON] et al. [166] \\ \cline{2-6}  & Magnetic nonlinearity & 100 & 6.4 & 5.5 & [PERSON] et al. [167] \\ \cline{2-6}  & Magnetic nonlinearity & 1000 & 10.2 & 0.49 & [PERSON] et al. [168] \\ \hline \multirow{4}{*}{Flutter} & Cubic stiffness nonlinearities & 100 & 18 & 106 & [PERSON] et al. [169] \\ \cline{2-6}  & Self-sustained inverted flag & 10,000 & 9 & 5 mW/cm\({}^{3}\) & [PERSON] et al. [172] \\ \cline{2-6}  & Magnetic force-induced nonlinearity & 1000 & 3.1 & 0.07 & [PERSON] et al. [175] \\ \cline{2-6}  & Structural nonlinearity & 100 & & 5.5 & [PERSON] et al. [177] \\ \cline{2-6}  & Structural nonlinearity & 250 & 15.16 & 1.27 & [PERSON] et al. [178] \\ \cline{2-6}  & Structural nonlinearity & 250 & 14 & 3.382 & [PERSON] et al. [179] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of nonlinear PE-FBEHs. Figure 12: Nonlinear PE-FEHs: (**a**) VIV piezo-magneto-elastic EH reproduced with permission from [153] Elsevier, 2017. (**b**) Self tunable airfoil EH [157]. (**c**) VIV-EH with nonlinear stiffness reproduced with permission from [159] Elsevier, 2024. (**d**) Y-shaped bistable PEH reproduced with permission from [162] Elsevier, 2018. (**e**) Galloping-based moving bluff body reproduced with permission from [166] Elsevier, 2021. (**f**) Tistable flutter-based PEH reproduced with permission from [181] Elsevier, 2024.