Nonlinear analysis and analog simulation of a piezoelectric buckled beam with fractional derivative

. In this article, an analog circuit for implementing fractional-order derivative and a harmonic balance method for a vibration energy harvesting system under pure sinusoidal vibration source is proposed in order to predict the system response. The objective of this paper is to discuss the performance of the system with fractional derivative and nonlinear damping ( μ b ). Bifurcation diagram, phase portrait and power spectral density (PSD) are provided to deeply characterize the dynamics of the system. These results are corroborated by the 0-1 test. The appearance of the chaotic vibrations reduces the instantaneous voltage. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim). The corresponding electronic circuit is designed, exhibiting periodic and chaotic behavior, in accord with numerical simulations. The impact of fractional derivative and nonlinear damping is presented with detail on the output voltage and power of the system. The agreement between numerical and analytical results justifies the efficiency of the analytical technique used. In addition, by combining the harmonic excitation with the random force, the stochastic resonance phenomenon occurs and improves the harvested energy. It emerges from these results that the order of fractional derivative μ and nonlinear damping μ b play an important role in the response of the system.