# Response Analysis of Asymmetric Monostable Harvesters Driven by Color Noise and Band-Limited Noise
## 1 Introduction
Simulated data showed that the BEH exhibited the phenomenon of stochastic resonance which can be applied to optimize the output power when knowing the variance of the excitation. [PERSON] et al. [22] experimentally studied the output of a magnetically coupled piezoelectric cantilever under the excitation of a 1/f vibration spectrum, and indicated that an increase of 50% in output voltage was observed when compared with its linear counterpart. Theoretically, [PERSON] et al. [23] approximately determined the output performance of a nonlinear piezoelectric energy harvester excited by Gaussian white noise excitations by an equivalent linearization method and numerical simulation demonstrated the effectiveness of the results. [PERSON] et al. [24] considered the response of a piezoelectric MEH by utilizing the stochastic averaging method. Agreements between the analytical results and Monte Carlo simulations verified the effectiveness of the proposed technique. Applying the Fokker-Plank-Kolmogorov (FPK) equation, [PERSON] [25] derived the exact joint probability density function of the response of a uni-modal electromagnetic harvester under Gaussian white noise excitation and showed that the nonlinearities in the stiffness do not provide any enhancement over the linear harvesters. Much effort has been devoted to evaluating the output performance of multistable energy harvesters with perfectly symmetric potential energy functions. However, it is difficult or even impossible to achieve a nonlinear energy harvester with perfectly symmetric potentials. [PERSON] [26] considered an asymmetric quartic potential in a BEH and indicated that the asymmetric potential has a great influence on the output. [PERSON] et al. [27] studied the asymmetric potential characterized by [PERSON] [28] and showed that the asymmetric potential has a positive effect on the MEH and a negative effect on the BEH. More recently, [PERSON] et al. [29] investigated the nonlinear dynamics of an asymmetric tristable harvester and demonstrated that the power depended on the asymmetry. [PERSON] et al. [30] studied the influence of the asymmetric potential on BEHs and indicated that the performance can be enhanced by inclining the system with a certain bias angle. Furthermore, [PERSON] et al. [31,32] investigated the response of monostable, bistable, and tistable piezoelectric energy harvesters under Gaussian white noise. Although the asymmetry in energy harvesters has been investigated extensively, the influence of asymmetric potentials on the output performance of MEHs under color noise and band-limited noise is still an open issue. Therefore, this paper focuses on the influence of asymmetric potential energy functions on the response of monostable energy harvesters (MEHs) subjected to color noise and band-limited noise. The method of moment differential equation was applied to determine the response of MEHs under color noise. The influence of system parameters on the output performance of the asymmetric MEHs was studied and numerical results agree well with the theoretical outcomes. For the band-limited noise, numerical investigations are undertaken and the influence of center frequency, frequency bandwidth, and the degree of asymmetry on the response was considered. The paper is organized as follows: in Section 2, the dynamic model of the asymmetric MEH is presented. Theoretical and numerical investigations of the influence of asymmetric potentials on MEH subjected to color noise are presented in Section 3 and the response of asymmetric MEH under band-limited noise excitation is considered in Section 4. In the final Section 5, the conclusion is provided.