Geometrically nonlinear model of piezoelectric wind energy harvesters based on vortex-induced vibration and galloping

The interaction between vortex-induced vibration (VIV) and galloping could enhance the performance of wind energy harvesters (WEHs). Though VIV-galloping interaction may cause large amplitude wind-induced vibrations, the effects of geometrical nonlinearity were not considered in the modeling of VIV-galloping interactive piezoelectric WEHs (PWEHs). In this work, based on the extended Hamilton's principle, a geometrically nonlinear model (GNM) of cantilevered PWEHs with VIV-galloping interaction was derived. The model includes both the transverse and axial aerodynamic forces, and considers the effect of the rotation of the bluff body on the aerodynamic forces. The aerodynamic coefficients were extracted by a piecewise polynomial fitting in a relatively large range of angle of attack for the square cross-sectional bluff body. Two flexible PWEH prototypes were fabricated and tested in a small wind tunnel to verify the proposed model. After the mechanical damping ratio of the low-coupling piezoelectric energy harvester prototypes were identified based on purely electrical measurements, the steady-state root mean square voltages of the prototypes with increasing wind speed were worked out using geometrically linear model (GLM) and the proposed GNM, respectively, and then compared with experiments. Both models can accurately predict the VIV-galloping interaction, but GNM is much more accurate than GLM at a relatively high wind speed. The proposed GNM provides a powerful tool to develop VIV-galloping interactive PWEHs.