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Self-excited chaotic dynamics of a nonlinear thermo-visco-elastic system that is subject to laser irradiation
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View: Figures


Image of FIG. 1.
FIG. 1.

Definition sketch.

Image of FIG. 2.
FIG. 2.

Top: Equilibrium position Xe as a function of normalized input power M for X0  = 0, s0  = 0.5, s1  = 0.66, Rm = 0.81, ξ = 0.43μm−1, and δ = 0.05. Unstable fixed points (dotted blue) connect saddles (defined by SN) between points with negative curvature. Stable (solid red) and unstable (dashed blue) fixed points connect saddles with Hopf bifurcations (defined by H). M(H1) = 1.923 defines transition from region I and II. Bottom: zoom on first (left) and second (right) SN points. M(H2) = 6.334 and M(H3) = 3.597 define transitions from IIIc to IIIb and IIIb to IIIa, respectively.

Image of FIG. 3.
FIG. 3.

Validation of the subcritical Hopf bifurcation in the Hane experiment2 for the parameter set in Fig. 2: stable limit-cycle (dashed red), stable fixed point (solid red), unstable limit-cycle (blue dots) vs. maximal limit-cycle measurement (green circles). Bottom: Periodic limit-cycle M = 2.0: time-series (left), power spectra (right).

Image of FIG. 4.
FIG. 4.

Strange attractor M = 8.0 (for parameter set in Fig 2): X(t) time-series (upper left), power spectrum (upper right), Z(X,Y) state-space (lower left), Poincaré map projection (lower right).

Image of FIG. 5.
FIG. 5.

Top: Bifurcation diagram (for parameter set in Fig. 2) of self-excited response depicted by Poincaré map magnitude (XPM ) for increasing values of power M. Bottom: time-series (left), and power spectra (right) of a periodic limit-cycle (M = 3.85) depicting an ultrasubharmonic of order m/n = 3/2, where limit-cycle frequency is f ∼ 0.16 (see Fig.3, bottom right) and dominant energy content is obtained at 2f/3 ∼ 0.105.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Self-excited chaotic dynamics of a nonlinear thermo-visco-elastic system that is subject to laser irradiation