预变形Jeffcott裂纹转子超谐波共振的动力学响应

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关键词：Jeffcott裂纹转子；预变形；多尺度法；动力学行为

中图分类号：TH113

DOI：10.3969/j.issn.1004-132X.2025.11.010

Abstract：Based on the theories of rotor dynamics and nonlinear dynamics，the dynamics response of 2/3 super-harmonic resonance of the system was studied for the rigidly supported horizontal Jefott cracked rotors underthe condition of1：1 internal resonance.Considering the gravity-induced pre-deformation effect and crack respiration behavior，a system dynamical equation with quadratic nonlinearity introduced by predeformation and cubic nonlinearity was established.The multi-scale method was used to derive the evolution equation of the system，and the influences of the changes of system parameters on the dynamics behaviors of the system were discussed in detail，and it is shown that with the increasing of crack depths and lateral damping coeficients，the frequency response curves of the system exhibit“frequency island”phenomenon.It is clarified that the square nonlinearity exhibits a softening effect on the system，while the cubic nonlinearity exhibits a hardening efect.Numerical integration of the system’s dynamics equation was conducted using the Runge-Kutta method to observe the jumping phenomenon，and the approximate solutions obtained through the multi-scale method were validated. The findings provide theoretical guidance for the nonlinear dynamics analysis of crack faults in Jeffcott rotor systems.

Key words： Jefott cracked rotor;pre-deformation；multiscale method;dynamics behavior

0 引言

在我国的电力和化学工业中，涡轮和压缩机是最重要和最普遍使用的机械设备。（剩余10710字）