Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities

This work is devoted to the robust analysis of the effects of geometric nonlinearities on the nonlinear dynamic behavior of rotating detuned (intentionally mistuned) bladed disks in presence of unintentional mistuning (simply called mistuning). Mistuning induces uncertainties in the computational model, which are taken into account by a probabilistic approach. This paper presents a series of novel results of the dynamic behavior of such rotating bladed disks exhibiting nonlinear geometric effects. The structural responses in the time domain are analyzed in the frequency domain. The frequency analysis exhibits responses outside the frequency band of excitation. The confidence region of the stochastic responses allows the robustness to be analyzed with respect to uncertainties and also allows physical insights to be given concerning the structural sensitivity. The bladed disk structure is made up of 24 blades for which several different detuned patterns are investigated with and without mistuning.

[1]  Christophe Pierre,et al.  Investigation of the combined effects of intentional and random mistuning on the forced response of bladed disks , 1998 .

[2]  Christophe Pierre,et al.  Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part I: Theoretical Models , 2001 .

[3]  Christian Soize,et al.  Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity , 2015, Journal of Sound and Vibration.

[4]  Christophe Pierre,et al.  Forced response of mistuned bladed disks using reduced-order modeling , 1996 .

[5]  Carlos Martel,et al.  Intentional mistuning effect in the forced response of rotors with aerodynamic damping , 2018, Journal of Sound and Vibration.

[6]  Christophe Pierre,et al.  Using Intentional Mistuning in the Design of Turbomachinery Rotors , 2002 .

[7]  Christian Soize,et al.  Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity , 2012 .

[8]  Fabrice Thouverez,et al.  Vibration Analysis of a Nonlinear System With Cyclic Symmetry , 2010 .

[9]  S. Michael Spottswood,et al.  A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures , 2013 .

[10]  Marc P. Mignolet,et al.  Optimization of Intentional Mistuning Patterns for the Reduction of the Forced Response Effects of Unintentional Mistuning: Formulation and Assessment , 2001 .

[11]  Ramana V. Grandhi,et al.  Probabilistic Analysis of Geometric Uncertainty Effects on Blade Modal Response , 2003 .

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

[13]  Jerry H. Griffin,et al.  A reduced order approach for the vibration of mistuned bladed disk assemblies , 1997 .

[14]  Christophe Pierre,et al.  Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration , 2003 .

[15]  Marc P. Mignolet,et al.  Optimization of Intentional Mistuning Patterns for the Mitigation of the Effects of Random Mistuning , 2008 .

[16]  Marc P. Mignolet,et al.  Identification of Mistuning Characteristics of Bladed Disks From Free Response Data— Part II , 1998 .

[17]  S. A. Tobias,et al.  The Influence of Dynamical Imperfection on the Vibration of Rotating Disks , 1957 .

[18]  Fredric F. Ehrlich,et al.  Handbook of Rotordynamics , 2004 .

[19]  Marc P. Mignolet,et al.  On the forced response of harmonically and partially mistuned bladed disks. Part II: Partial mistuning and applications , 2000 .

[20]  Eric Seinturier,et al.  Blade Manufacturing Tolerances Definition for a Mistuned Industrial Bladed Disk , 2005 .

[21]  Joerg R. Seume,et al.  Influence of Geometric Imperfections on Aerodynamic and Aeroelastic Behavior of a Compressor Blisk , 2017 .

[22]  Gene H. Golub,et al.  Matrix computations , 1983 .

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

[24]  Thomas A. Brenner,et al.  Acceleration techniques for reduced-order models based on proper orthogonal decomposition , 2008, J. Comput. Phys..

[25]  Christian Soize,et al.  Stochastic reduced order models for uncertain geometrically nonlinear dynamical systems , 2008, Computer Methods in Applied Mechanics and Engineering.

[26]  Benjamin Chouvion,et al.  Reduced-order modelling using nonlinear modes and triple nonlinear modal synthesis , 2018, Computers & Structures.

[27]  Giancarlo Genta,et al.  Vibration of Structures and Machines: Practical Aspects , 1992 .

[28]  Adrien Martin,et al.  Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities , 2018, Journal of Engineering for Gas Turbines and Power.

[29]  A. Vakakis Dynamics of a nonlinear periodic structure with cyclic symmetry , 1992 .

[30]  L. Sirovich Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[31]  Christophe Pierre,et al.  Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds , 1998 .

[32]  Bernd Beirow,et al.  Vibration analysis of an axial turbine blisk with optimized intentional mistuning pattern , 2019 .

[33]  Marc P. Mignolet,et al.  Optimization of Intentional Mistuning Patterns for the Mitigation of the Effects of Random Mistuning , 2014 .

[34]  Jean-Claude Golinval,et al.  Modeling of Uncertainties in Bladed Disks Using a Nonparametric Approach , 2014 .

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

[36]  Joerg R. Seume,et al.  Reduced Order Modeling of Mistuned Bladed Disks considering Aerodynamic Coupling and Mode Family Interaction , 2017 .

[37]  Christian Soize,et al.  An improvement of the uncertainty quantification in computational structural dynamics with nonlinear geometrical effects , 2017 .

[38]  J. H. Griffin,et al.  A Fundamental Model of Mistuning for a Single Family of Modes , 2002 .

[39]  Jerry H. Griffin,et al.  Maximum Bladed Disk Forced Response From Distortion of a Structural Mode , 2003 .

[40]  Christian Soize,et al.  Non-linear viscoelastodynamic equations of three-dimensional rotating structures in finite displacement and finite element discretization , 2004 .

[41]  Denis S. Whitehead,et al.  The Maximum Factor by Which Forced Vibration of Blades Can Increase Due to Mistuning , 1996 .

[42]  Moustapha Mbaye,et al.  Robust Analysis of Design in Vibration of Turbomachines , 2013 .

[43]  Denis Laxalde,et al.  Non-Linear Modal Analysis for Bladed Disks With Friction Contact Interfaces , 2008 .