针对失谐叶盘结构的受迫响应与叶片失谐之间的敏感性问题，提出了一种失谐叶盘最大响应幅值分别关于叶片频率失谐参数和叶片节点失谐质量的一阶和二阶灵敏度系数计算方法，以探究叶盘结构失谐参数对其最大响应幅值的影响。该方法立足于高保真失谐叶盘减缩建模和响应分析技术，直接对失谐叶盘结构的动力学方程进行推导获取其一阶和二阶灵敏度系数的数学表达式，未引入任何其他近似和简化计算措施，可以有效地求解高保真失谐叶盘最大响应幅值在不同激励频段、激励阶次和失谐形式下的灵敏度系数。该灵敏度分析方法在大规模高保真失谐叶盘结构模型上验证了其有效性。结果表明，与常规的数值差分灵敏度近似计算方法相比，本文提出的灵敏度分析方法在计算精度和计算效率方面具有巨大的优势，对进一步的失谐叶盘响应分析具有广泛的应用前景和通用性。
The forced response of bladed discs is very sensitive to random blade mistuning. This paper proposes an effective sensitivity analysis method to explore the impact of blade mistuning parameters on the maximum vibrational amplitude of mistuned bladed discs. This method is constructed based on the reduced-order model and a subsequent forced response analysis of mistuned bladed discs. Mathematical expressions of the first and second order sensitivity coefficients for the maximum blade vibrational amplitude with respect to blade frequency mistuning parameters and mistuning nodal mass are derived from the equations for motion of mistuned bladed discs, without any hypothesis or numerical simplification. The method proposed can be used to perform effective sensitivity analysis for bladed discs with any random blade mistuning pattern vibrating in different frequency bands under an engine order excitation. The method is numerically validated in a high-fidelity mistuned bladed disc model. It is shown that the proposed method has the advantages of high accuracy and computational efficiency over the method of finite difference approximation of the sensitivity coefficients. Benefiting from its versatility, the method proposed is expected to further contribute to the forced response analysis of mistuned bladed discs.
[1] 臧朝平, 兰海强. 失谐叶盘结构振动问题研究新进展[J]. 航空工程进展, 2011, 2(2):133-142. ZANG C P, LAN H Q. Advances in research vibration problem of mistuned blisk assemblies[J]. Advances in Aeronautical Science and Engineering, 2011, 2(2):133-142(in Chinese).[2] CASTANIER M P, PIERRE C. Modeling and analysis of mistuned bladed disk vibration:Current status and emerging directions[J]. Journal of Propulsion and Power, 2006, 22(2):384-396.[3] PIERRE C. Mode localization and eigenvalue loci veering phenomena in disordered structures[J]. Journal of Sound and Vibration, 1988, 126(3):485-502.[4] SLATER J C, MINKIEWICZ G R, BLAIR A J. Forced response of bladed disk assemblies-A survey[J]. Shock and Vibration Digest, 1999, 31(1):17-24.[5] 王建军, 姚建尧, 李其汉. 刚度随机失谐叶盘结构概率模态特性分析[J]. 航空动力学报, 2008, 23(2):256-262. WANG J J, YAO J Y, LI Q H. Probability characteristics of vibratory mode of bladed disk assemblies with random stiffness mistuning[J]. Journal of Aerospace Power, 2008, 23(2):256-262(in Chinese).[6] 李其汉, 王延荣, 王建军. 航空发动机叶片高周循环疲劳失效研究[J]. 航空发动机, 2003, 29(4):16-18. LI Q H, WANG Y R, WANG J J. Investigation of high cycle fatigue failures for the aero engine blades[J]. Aeroengine, 2003, 29(4):16-18(in Chinese).[7] WHITEHEAD D S. The maximum factor by which forced vibration of blades can increase due to mistuning[J]. Journal of Engineering for Gas Turbines and Power-transactions of the ASME, 1998, 120(1):115-119.[8] HAUG E J, EHLE P E. Second-order design sensitivity analysis of mechanical system dynamics[J]. International Journal for Numerical Methods in Engineering, 1982, 18(11):1699-1717.[9] HAFTKA R T. Second-order sensitivity derivatives in structural analysis[J]. AIAA Journal, 1982, 20(12):1765-1766.[10] HAFTKA R T, MROZ Z. First and second order sensitivity analysis of linear and nonlinear structures[J]. AIAA Journal, 1986, 24(7):1187-1192.[11] KOMKOV V, CHOI K K, HAUG E J. Design sensitivity analysis of structural systems[M]//Mathematics in Science and Engineering, Volume 177. Orlando, FL:Academic Press, 1986:381.[12] WANG B P. Eigenvalue sensitivity with respect to location of internal stiffness and mass attachments[J]. AIAA Journal, 1993, 31(4):791-794.[13] OGUAMANAM D C, LIU Z S, HANSEN J S. Natural frequency sensitivity analysis with respect to lumped mass location[J]. AIAA Journal, 1999, 37(8):928-932.[14] PETROV E P, IGLIN S P. Search of the worst and best mistuning patterns for vibration amplitudes of bladed disks by the optimization methods using sensitivity coefficients[C]//Proceedings of the 1st ASSMO UK Conference, Engineering Design Optimization. Ilkley:MCB University Press, 1999.[15] PETROV E P. A sensitivity-based method for direct stochastic analysis of nonlinear forced response for bladed disks with friction interfaces[J]. Journal of Engineering for Gas Turbines and Power, 2008, 130(2):022503.[16] 臧朝平, 段勇亮, E.P. PETROV. 失谐叶片轮盘的减缩建模及动力响应预测方法[J]. 航空学报, 2015, 36(10):3305-3315. ZANG C P, DUAN Y L, PETROV E P. Reduced-order modelling and dynamics response prediction method for mistuned bladed discs[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(10):3305-3315(in Chinese).[17] DUAN Y, ZANG C, PETROV E P. Forced response analysis of high-mode vibrations for mistuned bladed disks with effective reduced-order models[J]. Journal of Engineering for Gas Turbines and Power, 2016, 138(11):112502.[18] YANG M T, GRIFFIN J H. A reduced-order model of mistuning using a subset of nominal system modes:99-GT-288[R]. New York:ASME, 1999.[19] PETROV E P, SANLITURK K Y, EWINS D J. A new method for dynamic analysis of mistuned bladed disks based on the exact relationship between tuned and mistuned systems[J]. Journal of Engineering for Gas Turbines & Power, 2002, 124(3):586-597.[20] 王建军, 李其汉. 航空发动机失谐叶盘振动减缩建模与应用[M]. 北京:国防工业出版社, 2009:1-3. WANG J J, LI Q H. Methods and applications of reduction modeling for mistuned bladed disk in aero-engine[M]. Beijing:National Defense Industry Press, 2009:1-3(in Chinese).
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