Stochastic analysis of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation

Yang, Yong-Ge; Xu, Wei

doi:10.1007/s11071-018-4382-z

Cited by 35 publications

(20 citation statements)

References 41 publications

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“…Yet, to the authors' knowledge, only several researchers [25]- [28] considered the fractional-order energy harvesting systems. Based on the standard stochastic averaging method, Yang and Xu [28] investigated the stochastic response of mono-stable fractional-order vibration energy harvesting systems. However the procedure proposed by Yang and Xu [28] cannot be used to predict the influence of the nonlinear restoring force on the system responses.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the standard stochastic averaging method, Yang and Xu [28] investigated the stochastic response of mono-stable fractional-order vibration energy harvesting systems. However the procedure proposed by Yang and Xu [28] cannot be used to predict the influence of the nonlinear restoring force on the system responses. In order to resolve this limitation, combining the stochastic averaging method and generalized harmonic function, we put forward a method to investigate the piezoelectric energy harvesting system with fractional derivative element in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…In order to resolve this limitation, combining the stochastic averaging method and generalized harmonic function, we put forward a method to investigate the piezoelectric energy harvesting system with fractional derivative element in this paper. Figure 1 presents the simplified model of a piezoelectric energy harvesting system with fractional derivative element [14], [28], [29]. The motion equations are of the following form [14], [28], [29]:…”

Section: Introductionmentioning

confidence: 99%

“…Figure 1 presents the simplified model of a piezoelectric energy harvesting system with fractional derivative element [14], [28], [29]. The motion equations are of the following form [14], [28], [29]:…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Averaging for the Piezoelectric Energy Harvesting System With Fractional Derivative Element

Sun

Yang

2020

IEEE Access

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Combining the stochastic averaging method and generalized harmonic function, we propose a procedure to investigate the fractional-order energy harvesting system. First, we can obtain the approximately equivalent system by means of the generalized harmonic transformation; Second, the stochastic averaging method is utilized to get the approximate stationary solutions of the simplified system. Finally, In order to illustrate the accuracy of the developed scheme, two examples are carried out. The results show that the developed procedure has a satisfactory reliability. The influences of the intensity of noise excitation, the fractional order, the fractional coefficient and the nonlinear restoring force on the mean-square voltage (MSV) and mean output power (MOP) are also investigated.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Averaging for the Piezoelectric Energy Harvesting System With Fractional Derivative Element

Sun

Yang

2020

IEEE Access

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“…Wahi and Chatterjee studied effect of the delay and fractional derivative terms in oscillations of a resonator [14]. Yang and Xu used stochastic averaging to investigate the effects of fractional parameters on the output voltage of an energy harvester with fractional damping [15].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Plate on the Generalized Foundation with Fractional Damping Subjected to Random Excitation

Hosseinkhani

Younesian

Farhangdoust

2018

Mathematical Problems in Engineering

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Stochastic response of a plate on the generalized foundation driven by random excitation is solved in this paper. Governing differential equation is obtained by employing the Galerkin method. The generalized harmonic function technique is applied to the governing equation of motion. Using the stochastic averaging method (SAM), the system is approximated by the time homogeneous diffusive Markov process. Corresponding approximate stationary probability function is achieved by solving associated FokkerPlank-Kolmogorov (FPK). An analytical solution is presented for the stationary probability of the amplitude and velocity. Validity of the stationary probability is verified by Monte-Carlo simulation. Parametric study is carried out to investigate effects of foundation parameters and excitation intensity on the stationary probability function. It is found that the fractional properties act similar to the foundation stiffness and damping and can be employed as a new control parameter for the support design.

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Probabilistic solutions of a variable-mass system under random excitations

et al. 2020

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Stochastic analysis of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation

Cited by 35 publications

References 41 publications

Stochastic Averaging for the Piezoelectric Energy Harvesting System With Fractional Derivative Element

Stochastic Averaging for the Piezoelectric Energy Harvesting System With Fractional Derivative Element

Dynamic Analysis of a Plate on the Generalized Foundation with Fractional Damping Subjected to Random Excitation

Probabilistic solutions of a variable-mass system under random excitations

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