叶盘耦合振动转/静子叶片数与节径数关系

针对航空发动机中叶盘结构的共振分析问题，通过研究气体激励力和叶盘节径型振动在转子坐标系下的数学表达形式，利用叶盘结构共振时，气体激励力需要对叶盘系统做正功的条件，推导了叶盘发生共振时，节径数与转/静子叶片数应满足的关系式dm=kNv-nNb。通过3个数值算例对上述关系式进行了阐述:从气动功和谐响应分析的角度验证了当上述关系存在时，且激励频率等于结构固有频率时，叶盘系统会发生危害共振；同时指出，当上述变量不满足上述关系时，若激励频率等于叶盘结构的固有频率，也会引起部分叶片发生较大振动的可能。 

Relationship between rotor/vanes blade number andnodal diameter number of bladed-disk coupling vibration

Targeting the resonant analysis of aero-engine bladed-disk structure, by studying the mathematical formula of the gas excitation and nodal diameter vibration in the revolving coordinate and based on the positive work condition when the gas excitation acted on the bladed-disk structure, a relational expression dm=kNv-nNb describing the relationship between the number of nodal diameter and rotor/stator was deduced while the structure was in resonance. Three numerical examples were given to illustrate the above relation: from the perspective of aerodynamic work and harmonic response, a bladed-disk structure was in resonance while the above relation existed and the excited frequency was equal to structural natural frequency, and moreover, partial blades may be in serious vibration state while the above-mentioned frequency was equal even if the fore-mentioned relation was not satisfied.