Cubic nonlinear stiffness and quadratic nonlinear piezoelectrical coupling on the dynamic behaviour of an aeroelastic energy harvesting system

Resumo

Nonlinear aspects of energy harvesting have been extensively investigated in the last 10 years for two

main reasons: improve the accuracy of the mathematical models of systems that inherently present nonlinear be-
haviour, and to intentionally introduce nonlinear behaviour to the system in order to improve the harvesting perfor-
mance. In this paper, we show the contributions of cubic nonlinear stiffness and quadratic nonlinear piezoelectrical

coupling on the dynamic behaviour of an aeroelastic energy harvesting system. To analyse each case analytically
the method of multiple scales is used. The application of nonlinearity can make systems difficult to solve. Multiple
scales is an analytical method to provide an approximate expression of the response of a system. This method work
for small periodic finite movements in the vicinity of a equilibrium. One of the advantages of this method is that
it allows solving equations in the presence of damping and nonlinearity. Numerically, the response is calculated
using a 4th order Runge-Kutta method. The amplitude related to plunge, pitch and voltage degrees of freedom as
function of the wind speed is analysed for different values of cubic and quadratic nonlinearity. The results indicate
that amplitude decreases when cubic nonlinear stiffness and quadratic nonlinear piezoelectrical coupling increase.
It is important to observe that the results show good agreement in the LCO amplitudes only near the bifurcation.