Fig 1.
Schematic illustration of the quarter-car model (See Appendix A.1 for symbols and detaielsS1 File).
Fig 2.
Schematic illustration of half-car model (See Appendix A.2 inS1 File for symbols and details).
Table 1.
Value of parameters for quarter-car model.
Table 2.
Value of parameters for half-car model.
Fig 3.
Plots of (a) bifurcation diagram and (b) largest nonzero Lyapunov exponents of the system without delay [Eq. (2)] as a function of excitation amplitude d0.
The phase portraits of (c) period 1 (P1) at d0 = 0.015, (d) period 2 (P2) at d0 = 0.017, (e) QP at d0 = 0.02, and (f) chaos (C) at d0 = 0.025. The solid line (blue) is for trajectory and the dashed line (red) is for
.
Fig 4.
Plots of frequency response curves of (a) and (b)
.
Fig 5.
Plots of (a) the bifurcation diagram and (b) the time periods as a function of d0.
The time series of periodic motions (c) P1 at d0 = 0.01 and (d) P2 at d0 = 0.017.
Fig 6.
Plots of (a) the time series of Zs (solid line) and Zu (dashed line) and (b) the corresponding phase portrait at d0 = 0.01.
Fig 7.
Plots of (a) bifurcation diagram and (b) largest nonzero Lyapunov exponent as a function of τ at the fixed d0 = 0.025 and ε = 1.0.
The phase portraits of (c) QP at τ = 0.2, (d) period-2 P2 at τ = 0.35, and (e) period-1P1 at τ = 0.8. The solid line (blue) is for trajectory and the dashed line (red) is for
.
Fig 8.
Heatmap of the largest nonzero Lyapunov exponent λ1 at ε = 1.0.
Fig 9.
Plots of (a) bifurcation diagram and (b) time periods of period-i motion Ti as a function of τ at d0 = 0.025 and ε = 1.0.
Time series of (c) period-2 P2 at τ = 0.35 and (d) period-1 P1 at τ = 0.8.
Fig 10.
Plots of (a) time series Zs, and Zu and (b) phase portrait at ε = 1.0 and τ = 0.8.
Fig 11.
Plots of (a) bifurcation diagram and (b) largest nonzero Lyapunov exponent of the system without delay as a function of excitation amplitude d0.
The phase portrait of (c) P1 at d0 = 0.008, (d) P2 at d0 = 0.011, and (e) C at d0 = 0.025. The solid line (blue) is for trajectory and the dashed line (red) is for
.
Fig 12.
Plots of frequency response curves of (a) and (b)
.
Fig 13.
Plots of (a) bifurcation diagram and (b) time periods Ti as a function of d0, Time series of periodic motions (c) P1 at d0 = 0.008 and (d) P2 at d0 = 0.011.
Fig 14.
Plots of (a) time series of Zsf and Zsr and (b) corresponding phase portrait (b).
(c) Time series of Zsf and Zuf and (d) corresponding phase portrait at d0 = 0.008.
Fig 15.
Plots of (a) bifurcation diagram and (b) largest nonzero Lyapunov exponent as a function of τf = τr = τ at d0 = 0.025 and ε = 1.5.
The phase portraits of (c) Period-6 P6 at τ = 0.28, (d) Period-2 P2 at τ = 0.35, and (e) Period-1 P1 at τ = 0.6. The solid line (blue) is for trajectory and the dashed line (red) is for
.
Fig 16.
Heatmap of the largest nonzero Lyapunov exponentλ1 in the half-car model with delay.
Fig 17.
Plots of (a) bifurcation diagram and (b) time period of period-i motion Ti at d0 = 0.025 and ε = 1.5.
The time series Zuf of (c) P6 motion at τ = 0.3, (d) P2 motion at τ = 0.4, and (e) P1 motion at τ = 0.6.
Fig 18.
Plots of (a) time series of Zsf and Zsr and (b) corresponding phase portrait (b).
(c) Time series of Zsf and Zuf, and (d) corresponding phase portrait at εf = εr = 1.5 and τ = 0.6.
Fig 19.
Plot of (a) time series of Zsf and Zsr and (b) corresponding phase portrait (b).
(c) Time series of Zsf and Zuf and (d) corresponding phase portrait at ε = 1.5 and τ = 0.36.