THE EXISTENCE OF LIMIT CYCLES FOR THE SYSTEM X=Q(x,y),Y=P(x)

In [1], by a transformation on the Liemrd equation system suchihai the trajectories of (1)on both left and right half -planes change into thoseintegral curves of the new equation system merely on the right half-plane,A.F.Hilippov shows that under some certain conditions the stable limit cycles of system (1)must exist.Applying the Filippov’s method on the more generalized systemthis paper provides a sufficient condition for the existence of the stable limit cycles oftvstem (2).

Improving the process forming limit considering forming defects in the transitional region in local loading forming of Ti-alloy rib-web components

The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by forming defects in the transitional region.In this work,the feasibility of controlling forming defects and improving the process forming limit by adjusting die parameters is explored through finite element（FE） simulation.It is found that the common cavum and folding defects in the transitional region are significantly influenced by the fillet radii of left rib and middle rib,respectively.The cavum and folding defects can be effectively controlled by increasing the fillet radii of left rib and middle rib,respectively.The process forming limits considering forming defects in the transitional region are determined by the stepwise searching method under various die parameters.Moreover,the relationship between the process forming limit and die parameters is developed through the response surface methodology（RSM）.The developed RSM models suggest that increasing the fillet radii of left and middle ribs is effective to improve the process forming limit during local loading forming of rib-web components.The results will provide technical basis for the design of die parameters and the reduction amount,which is of great importance to control forming defects and improve the process forming limit in local loading forming of Ti-alloy large-scale rib-web components.

Study of an artificial boundary condition based on the damping-solvent extraction method

A new artificial boundary condition for time domain analysis of a structure-unlimited-foundation system was proposed.The boundary condition was based on the damping-solvent extraction method.The principle of the damping-solvent extraction method was described.An artificial boundary condition was then established by setting two spring-damper systems and one artificial damping limited region.A test example was developed to verify that the proposed boundary condition and model had high precision.Compared with the damping-solvent extraction method,this boundary condition is easier to be applied to finite element method(FEM)-based numerical calculations.