Randomly-disordered-periodic-induced chaos in a piezoelectric vibration energy harvester system with fractional-order physical properties

The chaotic behavior of the piezoelectric vibration energy harvester (VEH) system with fractional order physical properties under randomly disordered periodic excitations is investigated. By using random Melnikov method, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results indicate that the increase of the noise intensity will result in the occurrence of chaos and the changes of the possible chaotic region in phase space, which first enlarging and then shrinking with a change in trend. The threshold of amplitude of randomly disordered periodic for the onset of chaos is determined by the numerical calculation via the largest Lyapunov exponent. The effects of noise intensity on chaos are also investigated through the largest Lyapunov exponent, phase portraits, Poincaré maps. At the same time, the effects of intensity of random frequency on the mean square voltage are further discussed, which show that the square voltage is in positive proportion to the size of the chaotic region. It is demonstrated that the essential changes of the dynamical behavior of the piezoelectric energy harvester system with fractional order physical properties will occur through changing the noise intensity, which can not only induce or suppress the onset of the chaos, but also raise or reduce the mean square voltage. Finally, the 0-1 test of responses is used to quantify the responses of VEH system, which further supports the effects of noise intensity on chaotic behavior of the system.