A device capable of customizing nonlinear forces for vibration energy harvesting, vibration isolation, and nonlinear energy sink

Effect of Parameters on the Design of a Suspension System with Four Oblique Springs

“…In particular, it is found that such damping is proportional to the excitation frequency and linearly related to the cubic Figure 13: FRCs of the X-shaped suspension with QZS behaviour at large deflections for Y � 0.1(thin lines) and Y � 0.3 (thick lines), and different values of the system parameters as indicated by the circle (a), square (b), diamond (c), and star (d) in Figures 5 and 6. e damping is set according to equation (20). Stable analytical solutions are represented as solid lines; unstable analytical solutions are represented as dashed lines; numerical solutions are represented as empty circles; resonance peaks are represented as representative marker; and backbone curve are represented as dash-dotted line.…”

“…To validate the approximate expression in equation (20), this is plotted in Figure 12 as a dashed line and compared with the results from equation (15) for a relatively high and low value of excitation amplitude. It can be seen that despite the large variation of the excitation amplitude (10% and 50% of the displacement at the QZS point), the approximate expression captures the main trend for values of c greater that approximately − 0.5.…”

“…To better illustrate and validate the results presented above, the frequency response curves (FRCs) are plotted in Figures 13(a system parameters indicated by the markers in Figures 5 and 6. e FRCs of the system are solved in closed form from the amplitude-frequency equation reported in equation ( 13), which is quadratic in Ω 2 , and with damping ratio determined according to equation (20). e stability of the steadystate solutions is calculated by applying Floquet theory as detailed in [21] so that stable solutions are represented by solid lines and unstable solutions are represented by dashed lines in the FRCs of Figure 13.…”

“…It can be noted that the approximate FRCs capture the dynamic behaviour of the system reasonably well. Also, it can be seen that the effect of increasing the amplitude of excitation is to widen the bandwidth around the resonance frequency, but this frequency (and its corresponding displacement amplitude) is held constant through the proper selection of the damping according to equation (20). Animation S2 in the Supplementary Material illustrates the physical assembly of the suspension system corresponding to the case in Figure 13(b), when a sinusoidal base excitation at Ω � 1 is provided.…”

“…A simple and interesting relation between the excitation amplitude and the system damping is uncovered from the study of the frequency response. e analytical and numerical analysis presented in this paper allows a fundamental understanding of the nonlinear characteristics of the system, underpinning prospective pioneering applications which can be potentially attractive to the engineering community for vibration control issues at large [20].…”