Types of the jump phenomenon in the angular dependence of the noncollinear exchange bias

Based on the principle of minimal energy and the coherent rotation model, two types of the jump phenomena, complete and incomplete jump phenomenon, are proved to exist in the angular dependence of the exchange bias with noncollinear unidirectional and uniaxial anisotropies. It is found that the transition between complete and incomplete jump phenomena occurs on condition that the exchange-coupling constant exceeds a critical value. Additionally, two different modes of the magnetization rotation, the whole-plane rotation, and the half-plane rotation are present in the magnetization reversal process, and they are dependent on the direction of the external field. Furthermore, the equations of the critical angle, at which orientation the exchange bias field reaches a maximum value and the coercivity disappears, are also derived in this paper. The numerical calculations in this paper are consistent with the relevant experimental observations, indicating that our method to study the angular dependence of the exchange bias as well as the magnetization reversal behaviors is valid. Our discussion about the jump phenomenon, the critical angle, and the modes of the magnetization reversal can explain the observed differences in results between different experiments.

A PREDICT-CORRECT NUMERICAL INTEGRATION SCHEME FOR SOLVING NONLINEAR DYNAMIC EQUATIONS

A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation v = F（v, t） was transformed into the form as v = Hv ＋ f（v, t）. The nonlinear part f（v, t） was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.

Dynamic analysis of two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flow

The nonlinear aeroelastic response of a two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flows is investigated. The second-order piston theory is used to analyze a double-wedge airfoil. Then, the fold bifurcation and the amplitude jump phenomenon are detected by the averaging method and the multi-variable Floquet theory. The analyticall results are further verified by numerical simulations. Finally, the influence of the freeplay parameters on the aeroelastic response is analyzed in detail.

Influence of water and rock particle contents on the shear behaviour of a SRM

The contents of both water and rock particles are important factors affecting the mechanical strength of a soil–rock mixture(SRM)filled subgrade in the western mountainous area of China.Therefore,the purpose of this paper is to study the mechanisms of reconstituted landslide deposit samples with different water and rock particle contents by analysing the characteristics of shear strength,volumetric strain and‘jumping’phenomenon via large-scale direct shear tests.The results show that the influence of water content on shear strength is greater than the influence of rock particle content under a lower normal stress,and the results are reversed in the case of a higher normal stress.The effect of water content on the equivalent cohesion is bigger,especially for the sample with a high rock particle content.The friction angle of the specimen with same water content increases with the increasing rock particle content,but when the number of rock particles increases to a certain extent,there is a little effect on the friction angle.However,the friction angle decreases with increasing water content at the same rock particle content.Specimens with the same rock particle content change from dilation to compression with increasing water content.Finally,the continuous stage of the‘intense jumping’at different water content has been analysed.The‘jumping’phenomenon of samples with low water and rock particle content will first strengthen and then weaken the samples with increasing normal stress.