Vol. 4, No. 1 (2020): Regular Issue

In this paper, the global stability and bifurcations of equilibriums in the (2m)th-degree polynomial system are discussed for a better understanding the complexity of bifurcations and stability of equilibriums. The appearing and switching bifurcations for simple equilibriums are presented, and the appearing and switching bifurcations for higherorder equilibriums are discussed as well. The teethcomb-appearing, spraying-appearing, and sprinkler-spraying-appearing bifurcations for simple and higher-order equilibriums are presented. The antennaswitching bifurcations for simple and higher-order equilibriums are discussed and the parallel straw-bundle-switching and flower-bundleswitching bifurcations for simple and higher-order equilibriums are presented as well.

Aiming at the low classification accuracy of common decision tree C4.5 algorithm and the condition attribute problem of decision tree splitting point, a Bayesian decision tree algorithm combining ordinary decision tree C4.5 algorithm and naive Bayesian correlation algorithm is proposed in this paper. On this basis, the consistency test coefficient(kappa coefficient) is introduced to improve the correlation algorithm in the information gain rate in C4.5. Finally, the newly generated decision tree is pruned according to the most suitable splitting point. The improved algorithm proposed in this paper has a distinct improvement compared with the algorithm proposed in other literatures considering both time and accuracy.

As for the vibration problem of rotor system for large rotating machinery such as aero engines, a finite element model for dynamic similarity experiment system of rotor is established based on finite element theory. The effect of support stiffness and support position on the dynamic characteristics of the rotor system have been emphatically analyzed. Moreover, the effect of support stiffness on the dynamic characteristics of rotor system have been verified on the designed test rig. The results show that, under different support stiffness intervals, each order natural frequency of the rotor system has a different variation tendency with the support stiffness or position. In addition, the variation of the mode shapes with the support stiffness or position are closely related to the variation of the natural frequencies with the support stiffness and position. Combining with the practice, the natural frequencies of the rotor system can be reasonably designed and the harmful mode shapes can be avoided by adjusting the supporting characteristics of the rotor system.

The important focus of this work is to numerically examine the viscous dissipation and Ohmic heating effects on hydromagnetic flow of nanofluid over a porous stretching sheet with thermal radiation and heat generation/absorption filled with water-based copper and alumina nanofluids. Heat transfer features are investigated through convective conditions. Consider steady, nonlinear, two-dimensional of an incompressible, viscous and electrically conducting fluid past a porous stretching sheet in the presence variable magnetic field. To obtain meaningful results, we have taken thermal radiation in the heat transfer procedure. Governing nonlinear partial differential equation and they are transformed into an ordinary differential equation by using similarity transformation and the numerical solution is obtained by using Nachtsheim-Swigert shooting iteration scheme together with a fourth order Runge-Kutta integration method. Numerical results are obtained for the velocity and the temperature in the boundary layer region is studied in elaborate. Quantities of engineering interest such as skin friction coefficient and nusselt number are also obtained numerically and are tabulated.

The premixed piloted turbulent flame is studied numerically using Lagrangian coherent structures (LCS) to study and analyze the masstransport process from the viewpoint of nonlinear dynamic systems. The mass transport is shown to demonstrate a rich dynamical behavior. Firstly, the numerical simulation results show that the boundaries in the combustion field are delineated by the Lagrangian Coherent Structures. Secondly, the distribution of the attracting LCSs and the OH radical are compared to study the surface of the flame. Finally, the evolution of the LCS was tracked to analyze the vortexes and mass transport near the burner. The results show that the attracting LCS can be considered as a surface of the turbulent flame near the burner. The serial vortexes are regularly generated near the piloted jet, and they are gradually stretched and folded. These vortexes are attracted by the main jet as they move downward in the flow. The main jet goes into the flow field following an attracting LCS and moves forward attracting the piloted jet and the co-flow. However, fluid in the mainstream region has never entered into the piloted jet region, and this region does not exchange substance with the co-flow region. If the flow speed increases, air from the co-flow may pass through the LCS to mix with the material from the piloted jet region. Application of the LCS technique to study mass transport processes provides a new viewpoint for analyzing premixed piloted turbulent flames.