裂纹叶片频率转向和振型转换特性研究

推进技术 ›› 2015, Vol. 36 ›› Issue (4): 614-621.

裂纹叶片频率转向和振型转换特性研究

崔韦,王建军

北京航空航天大学能源与动力工程学院，北京 100191,北京航空航天大学能源与动力工程学院，北京 100191

发布日期:2021-08-15
作者简介:崔韦( 1985—)，男，博士生，研究领域为航空发动机强度振动。

FrequencyVeeringandModeShapeInteraction foraCrackedBlade

School of Energy and Power，Beihang University，Beijing 100191，China and School of Energy and Power，Beihang University，Beijing 100191，China

Published:2021-08-15

摘要/Abstract

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

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

崔韦,王建军. 裂纹叶片频率转向和振型转换特性研究[J]. 推进技术, 2015, 36(4): 614-621.

CUI Wei,WANG Jian-jun. FrequencyVeeringandModeShapeInteraction foraCrackedBlade[J]. Journal of Propulsion Technology, 2015, 36(4): 614-621.

参考文献

[1] Kuttler J R,Sigillito V G.On Curve Veering[J].Jour.nal of Sound and Vibration,1981,75(4): 585-588.
[2] Marugabandhu P,Griffin J H.A Reduced-Order Model for Evaluating the Effectof Rotational Speed on the Natu.ral Frequencies and Mode Shapes of Blades[J].Jour.nal of Engineering for Gas Turbines and Power,2003, 125(3): 772-776.
[3] 王建军,卿立伟,李其汉 .旋转叶片频率转向与振型转换特性[ J].航空动力学报, 2007,22(1): 8-11.
[4] 任兴民,南国防,秦洁,等 .航空发动机叶片“频率转向 ”特性研究[ J].西北工业大学学报, 2009,27(2): 269-273.
[5] Pierre C.Mode localization and Eigenvalue Loci Veer.ing Phenomena in Disordered Structures[J].Journal of Sound and Vibration,1988,126(3): 485-502.
[6] Kenyon J A,Griffin J H,Kim N E.Frequency VeeringEffects on Mistuned Bladed Disk Forced Response[J].Journal of Propulsion and Power,2004,20(5): 863-870.
[7] Kenyon J A,Griffin J H,Kim N E.Sensitivity of TunedBladed Disk Response to Frequency Veering[J].Jour.nal of Engineering for Gas Turbines and Power,2005, 127(4): 835-842.
[8] Bhat B B.Curve Veering: Inherent Behaviour of SomeVibrating Systems[J].Shock and Vibration,2000,7(4): 241-249.
[9] Perkins N C,Mote C D.Comments on Curve Veering inEigenvalue Problems[J].Journal of Sound and Vibra.tion,1986,106(3): 451-463.
[10] Lacarbonara W,Arafat H N,Nayfeh A H.Non-Linear Interactions in Imperfect Beams at Veering[J].Interna.tional Journal of Non-Linear Mechanics,2005,40(7): 987-1003.
[11] Saito A,Castanier M P,Pierre C.Estimation and Veer.ing Analysis of Nonlinear Resonant Frequencies of Cracked Plates[J].Journal of Sound and Vibration, 2009,326(3): 725-739.
[12] Ma C C, Huang C H.Experimental and NumericalAnalysis of Vibrating Cracked Plates at Resonant Fre.quencies[J].Experimental Mechanics,2001,41(1): 8-18.
[13] Andreaus U,Casini P,Vestroni F: Non-Linear Dynam.ics of a Cracked Cantilever Beam Under Harmonic Exci.tation[J].International Journal of Non-Linear Mechan.ics,2007,42(3): 566-575.
[14] 胡家顺,冯新,周晶.呼吸裂纹梁非线性动力特性研究[ J].振动与冲击, 2009,28(1)76-80,87.
[15] Wang J J,Cui W.Coupling Analysis of Vibration andFatigue Crack Propagation for a Breathing Cracked Beam[J].Applied Mechanics and Materials,2012,164: 338-343.
[16] Shaw S W,Holmes P J.A Periodically Forced Piece.wise Linear Oscillator[J].Journal of Sound and Vibra.tion,1983,90(1): 129-155.
[17] Chu Y C,Shen M H H.Analysis of Forced Bilinear Os.cillators and the Application to Cracked Beam Dynamics[J].AIAA Journal.1992,30(10): 2512-2519.
[18] Chati M,Rand R,Mukherjee S.Modal Analysis of a Cracked Beam[J].Journal of Sound and Vibration, 1997,207(2): 249-270.
[19] Allemang R J.Investigation of Some Multiple Input/Out.put Frequency Response Function Experimental ModalAnalysis Techniques[J].Dissertation Abstracts Interna.tional Part B: Science and Engineering,1981,41(10).
[20] Allemang R J,Brown D L.A Correlation Coefficient for Modal Vector Analysis[C].Orlando: Proceedings of the 1st International Modal Analysis Conference,SEM,1982, 1: 110-116.
[21] 郭雪莲 .叶轮机叶片流致激励振动阻尼的研究[ D].北京 :北京航空航天大学, 2013.(编辑:史亚红)* 收稿日期:2014-02-13；修订日期:2014-05-16。作者简介:崔韦( 1985—),男,博士生,研究领域为航空发动机强度振动。 E-mail:cuiwei@sjp.buaa.edu.cn