We investigate the effects of spin-flip scattering on the Hall transport and the spectral properties of gapped Dirac fermions. We find that in the weak scattering regime, the Berry curvature distribution is dramatically compressed in the electronic energy spectrum, becoming singular at band edges. As a result the Hall conductivity has a sudden jump (or drop) of e 2 /(2h) when the Fermi energy sweeps across the band edges, and otherwise is a constant quantized in units of e 2 /(2h). The spectral properties such as the density of states and the spin polarization are also greatly enhanced near band edges. Possible experimental methods to detect these effects are discussed.

Fatigue crack in a rotary shaft is a common failure observed in rotor systems. Since vibration of the shaft causes alternating fatigue loads, the crack propagates slowly. Meanwhile, the propagating crack may cause nonlinear or unstable vibration of the rotor system. In fact, growth of the crack and vibration of the shaft are coupled with each other. Hence, it is necessary to study the fatigue degradation behavior of the cracked rotor accounting for this coupling effect. In this paper, a coupling model of rotor vibration and crack growth is established through dynamic theory and fracture mechanics, and a sequential iterative procedure is proposed to solve the coupling model. Then, the competing degradation failure mode of the cracked rotor is analyzed with regard to the rapid crack growth failure and the unstable vibration failure. And degradation measures are proposed based on the competing degradation failure criterion. At last, degradation behaviors with the coupling effect of nonlinear vibration behavior and multiple parameters including rotation speed, unbalance eccentricity and orientation angle, and damping are investigated by numerical simulation. The results indicate that nonlinear vibration behavior and multiple parameters have considerable influence on the degradation behaviors, which present complex regularity. The findings are of significance to guide the safety design of the rotor system for long time operation and help to the further research on prognostics and lifetime prediction.

Mechanical structures in service are often subjected to irregular loads, which are typically idealized as stationary random processes. However, the service loads in real applications are often nonstationary ones, in which case conventional frequency‐domain methods are no longer applicable. Here, a novel frequency‐domain approach based on empirical mode decomposition is developed for the fatigue analysis of nonstationary processes. A simplified approach is introduced to calculate the rainflow cycle distributions of non‐Gaussian intrinsic mode functions. Two typical nonstationary processes in engineering practice are simulated numerically to validate the proposed method. The proposed method is applied to fatigue life estimation of a dynamical structure under nonstationary excitations. Reliable life estimations are obtained within much less computation time than the time‐domain method. The results verify the applicability and effectiveness of the proposed method for the fatigue analysis of nonstationary processes.