Vibratory behavior prediction of mistuned stator vane clusters: An industrial application

Abstract Geometric and material dispersions of bladed disks imply some mistuning effects, which result in both the loss of cyclic symmetry properties and a vibratory response amplification in areas of high modal density. These conditions complicate the prediction of vibratory behavior, causing high modal density and extreme sensitivity to mistuning. A non-intrusive spectral stochastic method has been developed to predict the vibratory behavior of a mistuned stator vane. To apply this method to an industrial model, a Karhunen-Loeve expansion and a double modal synthesis method have been combined with the stochastic method. The complete method was first tested on a simple academic model and then on an industrial stator vane sector.

[1]  I. Papaioannou,et al.  Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion , 2014 .

[2]  K. Binder,et al.  Monte Carlo Simulation in Statistical Physics , 1992, Graduate Texts in Physics.

[3]  Michał Kleiber,et al.  The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation , 1993 .

[4]  I. Elishakoff,et al.  Convex models of uncertainty in applied mechanics , 1990 .

[6]  Fabrice Thouverez,et al.  Mistuning identification for industrial blisks based on the best achievable eigenvector , 2006 .

[7]  D. S. Whitehead,et al.  Effect of Mistuning on the Vibration of Turbo-Machine Blades Induced by Wakes: , 1966 .

[8]  W. A. Benfield,et al.  Vibration Analysis of Structures by Component Mode Substitution , 1971 .

[9]  Roy R. Craig,et al.  Substructure coupling for dynamic analysis and testing , 1977 .

[10]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[11]  Fabrice Thouverez,et al.  A Simplified Method for Predicting the Average Vibratory Response of Mistuned Clustered Stator Vanes , 2014 .

[12]  Denis Laxalde,et al.  Mistuning Identification and Model Updating of an Industrial Blisk , 2007 .

[13]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[14]  R. Craig,et al.  Free-interface methods of substructure coupling for dynamic analysis , 1976 .

[15]  D. L. Thomas.  Dynamics of rotationally periodic structures , 1979 .

[16]  Christian Soize,et al.  Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks , 2004 .

[17]  S. Wold,et al.  The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses , 1984 .

[18]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[19]  Christophe Pierre,et al.  Strong Mode Localization in Nearly Periodic Disordered Structures , 1989 .

[20]  Fabrice Thouverez,et al.  Vibratory Behavior Prediction of a Mistuned Clustered Stator Vane: Non-Intrusive Stochastic Methods , 2015 .

[21]  A. Savitzky,et al.  Smoothing and Differentiation of Data by Simplified Least Squares Procedures. , 1964 .

[22]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[23]  W. F. Bauer,et al.  The Monte Carlo Method , 1958 .

[24]  J. Renaud.  Numerical Optimization, Theoretical and Practical Aspects— , 2006, IEEE Transactions on Automatic Control.

[25]  F. Thouverez,et al.  ANALYSIS OF MECHANICAL SYSTEMS USING INTERVAL COMPUTATIONS APPLIED TO FINITE ELEMENT METHODS , 2001 .

[27]  Ana C. Matos.  Recursive computation of Padé–Legendre approximants and some acceleration properties , 2001, Numerische Mathematik.

[28]  Laurent Blanc,et al.  Numerical Application of Double Modal Synthesis to an Industrial Mistuned Clustered Stator Vane and Experimental Validation , 2016 .

[29]  D. J. Ewins,et al.  The effects of detuning upon the forced vibrations of bladed disks , 1969 .

[30]  R. Valid,et al.  Théorie et calcul statique et dynamique des structures à symétries cycliques , 1985 .

[31]  F. Thouverez,et al.  Analysis of stochastic structures : Perturbation method and projection on homogeneous chaos , 1999 .

[32]  N. Wiener.  The Homogeneous Chaos , 1938 .

[33]  Christian Soize.  A nonparametric model of random uncertainties for reduced matrix models in structural dynamics , 2000 .

[34]  S. J. Wildheim.  Excitation of Rotationally Periodic Structures , 1979 .

[35]  R. C. F. Dye,et al.  Vibration Amplitudes of Compressor Blades Resulting From Scatter in Blade Natural Frequencies , 1969 .

[36]  A. Nouy.  Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations , 2009 .