Multiple scale analysis of energy harvesting in aeroelastic system in flutter condition

Resumo

The ever increasing need for efficient, environmental-friendly and sustainable energy sources has pro-
pelled the study of energy harvesting and its applications in many fields of engineering in the last decade. Nonlinear

aspects of energy harvesting have been extensively investigated for two main reasons: improve the accuracy of the

mathematical models of systems that inherently present nonlinear behaviour, and to intentionally introduce non-
linear behaviour to the system in order to improve the harvesting performance. Electrical nonlinear aspects can

have large influence on the harvesting device. Investigations of the effect of quadratic nonlinear piezoelectrical
coupling showed that the amount of harvested power can be significantly influenced. In this paper, we show the
contributions of cubic nonlinear stiffness on the dynamic behaviour of an aeroelastic energy harvesting system.
Analytically, each case is analysed using the method of multiple scales. The first case is a linear system with
finite degrees of freedom, the second case evaluates forced oscillations of system having cubic nonlinearity. We
relate natural frequencies present in the system and target energy transfers (TET). TET uses non-linear modes and
internal resonance to transfer vibration energy, passively. Numerically, the response is calculated using a 4th order
Runge-Kutta method. The results for the analysed system indicate that cubic nonlinear stiffness has more influence
in increasing flutter speed than increasing electrical power.