Ut voltage more than a wide selection of frequency in Figure 7(b
Ut voltage over a wide array of frequency in Figure 7(b2). Compared with DR, the amplitudes of frequency components of EMR decrease, in particular within the frequencies three and five.Appl. Sci. 2021, 11,9 ofFigure five. DR and EMR ( = 0.01) for =1.5. (a) Phase portraits; (b) Time history on the output voltage. The blue dots and red dots are obtained beneath the initial situations (IC-1) and (IC-2), respectively.Figure 6. DR and EMR ( = 0.01) for =0.9. (a) Phase portraits of DR; (b) Phase portraits of EMR ( = 0.01). (c) RMS voltage of DR and EMR ( = 0.01). The blue dots and red dots are obtained under the initial circumstances (IC-1) and (IC-2), respectively.Figure 7. DR and EMR ( = 0.01) for =0.01. (a1,a2) Time history of your output voltage of DR and EMR ( = 0.01); (b1,b2) Spectrum in the output voltage of DR and EMR ( = 0.01).The stochastic behavior of TEH with = 0.01 has been investigated above. Then, various values of are employed to observe how is about the influence below differentAppl. Sci. 2021, 11,ten ofintensities. It is actually clearly that the bigger the intensity is, the wider the interval matching the positive TLE of EMR is, as shown in Figure 8.Figure eight. The TLE with all the variation of damping coefficient under various intensities; (a) is obtained beneath the initial condition IC-1; (b) is obtained below the initial situation IC-2.4.two. Influence of the Electromechanical CFT8634 site coupling Coefficient The electromechanical coupling coefficient plays a key role in the behavior of TEH, so we take into account because the bifurcation parameter. Let = -4.five, = -4.5, = two.five, = 0.2, A = 1.2, = 0.9, = 0.5 and = 0.01, the multivalued bifurcation diagrams and corresponding TLE of DR and EMR are shown in Figure 9(a1,a2), respectively. When 0.77, DR keeps the LY294002 Casein Kinase periodic motion, but EMR enters into transient chaotic motion on account of the influence in the uncertain parameter. Immediately after decreases towards the crucial worth about 0.52, DR undergoes several period doubling bifurcation cascades and lastly becomes chaotic in Figure 9(a1), exactly where the corresponding TLE of DR gradually modifications from unfavorable to constructive. Instead, the crisis from periodic to chaotic motion is often clearly observed for EMR along with the TLE of EMR suddenly modifications from damaging to positive inside 0.46 0.52. Besides, the harvester below the initial situation IC-3 leaves the chaotic region firstly, which is usually seen more clearly in Figure 9(b2).Figure 9. Bifurcation diagrams and also the TLE with the variation of electromechanical coupling coefficient . (a1,a2) Multivalued bifurcation diagram of DR and EMR ( = 0.01); (b1,b2) Multivalued TLE of DR and EMR ( = 0.01). The blue dots and red dots are obtained below the initial conditions [ x0 , x1 , x2 , x3 , x4 ] = [-1.0, 0, 0, 0, 0], [ x0 , x1 , x2 , x3 , x4 ] = [-1.0, 0, 0, 0, 0], [v0 , v1 , v2 , v3 , v4 ] = [1.0, 0, 0, 0, 0](IC-3) and [ x0 , x1 , x2 , x3 , x4 ] = [-0.5, 0, 0, 0, 0], [ x0 , x1 , x2 , x3 , x4 ] = [1.0, 0, 0, 0, 0], [v0 , v1 , v2 , v3 , v4 ] = [1.0, 0, 0, 0, 0](IC-4), respectively.Specifically, when = 0.51, DR keeps 2T-period motion for distinct initial circumstances in Figure 10a. As we take the stochastic intensity = 0.01 in Figure 10b, there is certainly nearly no distinction among DR and EMR using the initial situation IC-4, but EMR with the initial situation IC-3 becomes chaotic. This indicates that the dynamic behavior of TEH is sensitive towards the initial circumstances around the given parameters. In addition, as is enhanced toAppl. Sci. 2021, 11,11 of0.1 in Figure 10c, the program respon.
