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Considering the two kinds of nonlinear constraints of rolling mill hydraulic cylinder, spring force and friction force, the vibration model of rolling mill system is established. The amplitude frequency response equations are obtained by using the average method. Comparing the time history curves of vertical vibration displacement of rolling mill system under the nonlinear spring force and friction force, the amplitude frequency characteristic curves are simulated. The external excitation amplitude is viewed as the bifurcation parameter, and the system bifurcation response changing with the external excitation amplitude is analyzed. The influence of the external excitation amplitude on the system stability is studied. The results indicate that the increase of the nonlinear spring force makes the rolling mill system’s unstable area to become wider, and the influence on the rolling mill system of nonlinear friction force behaves as the damping characteristics; the vibration of rolling mill system is alternating between the periodic, period-doubling, and the chaotic motion. The research results provide a theoretical support for restraining the vibration of the rolling mill system in the actual production process.

An all-solid dispersion-compensating photonic crystal fiber based on mode coupling mechanism in dual-concentric core has been proposed. The mode coupling characteristics, dispersion, confinement loss of the fiber, and the influence on dispersion of some structure parameters are simulated by full-vector finite element method. By using the relationship between phase matching wavelengths and coupling strength with the change of fiber microstructure parameters, an all-solid dual-concentric-core dispersion-compensating photonic crystal fiber is presented. The structure parameters on dispersion characteristic are investigated. The results demonstrate that the proposed fiber has a large negative dispersion value 8465 ps/(nm·km) at 1550 nm. The effective mode area and the splicing loss to the standard single mode fiber are 12.8 μm2 and 1.89 dB at 1550 nm, respectively. At 1550 nm, the confinement loss is less than 1 × 10−3 dB/km and the bending loss with 2 cm bending diameter is less than 1 × 10−2 dB/km.