In this paper,the response characteristics of dry friction backward whirl of a general rotor/stator model,which accounts for both the dynamics of the rotor and the stator as well as the friction and the deformation at the contact surfaces,are investigated.The existence boundaries and the whirl frequencies of the dry friction backward whirl are determined analytically.It is found that there are two or three existence boundaries of the dry friction backward whirl that usually form two existence regions,either standing completely separately,or overlapping each other partly,or one containing the other completely,depending upon the system parameters.The whirl frequencies in the two existence regions are quite different and may jump between the lower and the higher values with the variation of the rotating speed.The results have been found to have good correspondence in the related rotor/stator rubbing experiments.
JIANG Jun,SHANG ZhiYong & HONG Ling MOE Key Laboratory of Strength and Vibration,Xi’an Jiaotong University,Xi’an 710049,China
A crisis in a Duffing-van del Pol system with fuzzy uncertainties is studied by means of the fuzzy generalised cell mapping （FGCM） method. A crisis happens when two fuzzy attractors collide simultaneously with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical point. The two fuzzy attractors merge discontinuously to form one large fuzzy attractor after a crisis. A fuzzy attractor is characterized by its global topology and membership function. A fuzzy saddle with a complicated pattern of several disjoint segments is observed in phase space. It leads to a discontinuous merging crisis of fuzzy attractors. We illustrate this crisis event by considering a fixed point under additive and multiplicative fuzzy noise. Such a crisis is fuzzy noise-induced effects which cannot be seen in deterministic systems.
This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.
Jun Jiang) MOE Key Laboratory of Strength and Vibration, Xi’an Jiaotong University, Xi’an 710079, China
