Abstract: Frequency veering and mode shape interaction of a cracked cantilevered plate blade are simulatedusing modal analysis and nonlinear analysis in finite element method. Firstly，frequency veering and shape inter.action due to crack length changing are investigated in linear modal analysis using open crack model. The processof shape interaction is quantitatively studied by modal assurance criterion in veering region. Then a bilinear crackmodel is established by considering crack closure effect. Nonlinear resonant frequencies are calculated using bi.linear crack model. The differences of veering results using linear and nonlinear approaches are discussed. Atlast，a contact FEM crack model is used to verify resonant frequencies of bending，twisting and in-plane bendingmodes between open model and bilinear model by forced response sweeping calculation.

Key words: Cracked blade；Frequency veering；Mode shape interaction；Modal analysis；Bilinear frequency； Modal assurance criterion

摘要： 基于有限元法对裂纹悬臂平板叶片的频率转向和振型转换特性进行了线性和非线性研究。首先使用张开型裂纹模型通过线性模态分析研究了裂纹长度变化引起的频率转向和振型转换问题，使用模态置信因子定量分析了频率转向区内振型的渐变过程。而后考虑裂纹闭合效应，建立了裂纹平板的双线性模型，使用张开型和闭合型模型线性分析结果计算得到双线性频率，其中张开型和闭合型裂纹振型通过模态相关性分析进行匹配。计算了裂纹叶片双线性频率，分析了非线性频率转向特性与线性分析结果的差异。最后使用接触有限元模型瞬态响应扫频计算得到非线性共振频率，对张开型模型和双线性模型在典型弯曲、扭转和面内弯曲模态的共振频率进行了验证。

关键词: 裂纹叶片；频率转向；振型转换；模态分析；双线性频率；模态置信因子