Ricerc@Sapienza

In this work, the nonlinear response of a PVDF vibration piezoelectric energy harvester (EH) is analyzed using a novel hybrid multiscale approach. At the system scale, the resulting set of fractional differential equations (FDE) comes out from the assumption of a fractional order current-voltage relationship for the electrical capacitance in the circuit and a fractional power law in the nonlinear mechanical spring element. The constitutive model of this spring arises from the microscale analysis of the PVDF EH behavior under increasing static forces. At this scale a distributed model is employed and the finite element method is used for the discretization. In particular for the restoring force, a Duffing type fractional order power law is identified with the purpose to approximate the finite element based capacity curves analytically. Once the linear and nonlinear stiffness coefficients and the fractional order parameter are obtained minimizing the overall error, the final set of FDEs is solved. An Oustaloup recursive filter is used to approximate the fractional-order differentiators in the frequency range of interest. Results highlight both the influence of the fractance capacitor and the order of the time derivative on the amplitude of the mechanical vibrations around the resonance condition. Moreover the effects on the power output and the energy efficiency are also discussed.