# Response Analysis of Asymmetric Monostable Harvesters Driven by Color Noise and Band-Limited Noise
## 4 Response of the Asymmetric MEHs under Band-Limited Noise  
In this section, we focus on considering the response characteristics of asymmetric potential MEHs subjected to band-limited noise excitation. Before discussing the response under band-limited noise excitation, the response under harmonic excitation is emphasized. Under an up-sweep frequency excitation with a level of 0.2, the voltage responses of four MEHs with different values of the quadratic coefficient are shown in Figure 9a. The MEHs could generate a larger voltage in a wider frequency range. With the increase in asymmetric degree, the response bandwidth was slightly enlarged around the cut-off frequency (COF-1) while the response amplitude was slightly decreased. For a down-sweep frequency excitation, the response voltage of the four MEHs was depicted in Figure 9b. The results show that the response frequency band and cut-off frequency (COF-2) shifts to the lower frequencies with an increase in the asymmetry. This analysis demonstrates that the response of asymmetric MEHs exhibits the property of multiple solutions between COF-1 and COF-2. Under band-limited noise excitation, the property of multiple solutions of MEHs cannot be achieved, and consequently, the response frequency is mainly distributed in lower frequencies. Figure 8: PDF Probability density function of dimensionless displacement for different values of quadratic coefficient. Figure 7: Voltage responses of asymmetric MEHs with different values of quadratic coefficients (**a–d**). In the numerical simulations, the band-limited noise used for excitation was obtained by passing the Gaussian white noise with certain noise intensity through a band-pass filter. For a certain frequency bandwidth of 0.05, Figure 10 illustrates the influence of center frequency (CF) on the average output power of the asymmetric MEH (\(\beta=1\)) excited by band-limited noise with different noise intensities. Given a certain center frequency, the asymmetric MEH generates a larger average output power when excited by band-limited noise with larger noise intensity. With the center frequency shifting to high frequency, the average output power of the asymmetric MEH first increases and then decreases, and achieves its maximum value around the COF-2. On the whole, it is observed that the asymmetric MEH outputs larger power in a wide frequency range when subjected to band-limited noise with larger noise intensity, and the characteristic is similar to the response of MEH under harmonic excitation. For a certain center frequency of 0.18, which is near the COF-2, the effect of frequency bandwidth on the output performance of the asymmetric MEH excited by band-limited noise with different noise intensity is diagramed in Figure 11. For a lower excitation intensity of 0.01, the average output power quickly increases to a certain value and then basically remains unchanged with the center frequency shifting to high frequency. With the increase in noise intensity, the trend of output power increasing with the increase in frequency bandwidth becomes slow. Of course, the MEH generates larger output power for larger noise intensity. Figure 10: Influence of center frequency on the output performance of the asymmetric MEH excited by band-limited noise with different noise intensity (\(\Delta=0.05\)). Figure 9: Influence of quadratic coefficient on the response frequency band of the asymmetric MEH under harmonic excitation with a level of 0.2: **(a)** up-sweep frequency; **(b)** down-sweep frequency. For a noise intensity of 0.05, we investigated the influence of center frequency on the output of the asymmetric MEH excited by band-limited noise with different frequency bandwidths, and the simulated results are illustrated in Figure 12. For a given frequency bandwidth, the average output power increases first and then decreases with the center frequency moving to high frequencies, and the average output achieved maximum values near the COF-2.