Identification of Mistuning Characteristics of Bladed Disks From Free Response Data— Part II

1999 ◽  
Vol 123 (2) ◽  
pp. 404-411 ◽  
Author(s):  
A. J. Rivas-Guerra ◽  
M. P. Mignolet ◽  
J. P. Delor
Keyword(s):  
Maximum Likelihood ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Forced Response ◽  
Likelihood Method ◽  
Mode Shapes ◽  
Free Response ◽  
Bladed Disks ◽  
Response Data ◽  
Block Test

The focus of the present two-part investigation is on the estimation of the dynamic properties, i.e., masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. In this second part of the investigation, the maximum likelihood method (ML) will first be revisited and a thorough assessment of its reliability in a wide variety of conditions, including the presence of measurement noise, different distributions of blade structural properties, etc., will be conducted. Then, a technique that provides a bridge between the two identification methods introduced in Part I, i.e., the random modal stiffnesses (RMS) and maximum likelihood (ML) approaches, will be presented. This technique, termed the improved random modal stiffnesses (IRMS) method is based on the maximum likelihood concepts but yields a mistuning model similar to that of the random modal stiffnesses technique. Finally, the accuracy of the RMS, ML, and IRMS methods in predicting the forced response statistics of mistuned bladed disks will be investigated in the presence of close blade alone natural frequencies.

scholarly journals Identification of Mistuning Characteristics of Bladed Disks From Free Response Data

1998 ◽  
Author(s):  
Marc P. Mignolet ◽  
Alejandro Rivas-Guerra
Keyword(s):  
Dynamic Models ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Identification Problem ◽  
Forced Response ◽  
Mode Shapes ◽  
Likelihood Principle ◽  
Bladed Disks ◽  
Block Test

The focus of the present investigation is on the estimation of the dynamic properties, i.e. masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. Two distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to insure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade-to-blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function”. The accuracy of these two techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.

Identification of Mistuning Characteristics of Bladed Disks From Free Response Data — Part II

1999 ◽  
Author(s):  
Marc P. Mignolet ◽  
Jason P. Delor ◽  
Alejandro Rivas-Guerra
Keyword(s):  
Dynamic Models ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Identification Problem ◽  
Forced Response ◽  
Mode Shapes ◽  
Likelihood Principle ◽  
Bladed Disks ◽  
Block Test

The focus of the present investigation is on the estimation of the dynamic properties, i.e. masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. Three distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to insure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade-to-blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function”. Finally, the third approach provides a bridge between the first two methods being based on the second but yielding a mistuning model similar to that of the first approach. The accuracy of these three techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.

Identification of Mistuning Characteristics of Bladed Disks From Free Response Data—Part I

1999 ◽  
Vol 123 (2) ◽  
pp. 395-403 ◽  
Author(s):  
M. P. Mignolet ◽  
A. J. Rivas-Guerra ◽  
J. P. Delor
Keyword(s):  
Dynamic Models ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Identification Problem ◽  
Forced Response ◽  
Mode Shapes ◽  
Likelihood Principle ◽  
Bladed Disks ◽  
Block Test

The focus of the present two-part investigation is on the estimation of the dynamic properties, i.e., masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example, in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. In this first part of the investigation, two distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to ensure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade to blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function.” The accuracy of these two techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.

High Fidelity Transient Forced Response Analysis of Mistuned Bladed Disks Under Complex Excitation and Variable Rotation Speeds

2020 ◽  
Author(s):  
Jing Tong ◽  
Chaoping Zang ◽  
Evgeny Petrov
Keyword(s):  
Large Scale ◽  
Rotation Speed ◽  
Dynamic Properties ◽  
Spectral Composition ◽  
Forced Response ◽  
Mode Shapes ◽  
Response Analysis ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Amplitude Amplification

Abstract An effective method is developed for the efficient calculation of the transient vibration response for mistuned bladed disks under complex excitation and varying rotation speeds. The method uses the large-scale finite element modelling of the bladed disks allowing the accurate description of the dynamic properties of the mistuned bladed disks. The realistic distributions of the excitation forces are considered, which resulted in the multiharmonic excitation loads. The transient response calculation is based on the analytically derived expressions for the transient forced response and the effective method used for the model reduction. The effects of the varying rotation speed on the natural frequencies and mode shapes of the mistuned bladed disk and its effects on the amplitude and the spectral composition of the loading are allowed for. The different functions of the rotation speed variation can be analyzed. Numerical studies of the transient forced response and the amplitude amplification in mistuned bladed disks are performed when the resonance regimes are passed during gas-turbine engine acceleration or deceleration. The effects of different types of excitation force and mistuning on transient amplitude amplification are illustrated by a large number of the computational results and comparative analysis. These results and analysis of transient forced response are shown on an example of a realistic mistuned bladed disk.

scholarly journals Forced Response Analysis of High-Mode Vibrations for Mistuned Bladed Disks With Effective Reduced-Order Models

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Yongliang Duan ◽  
Chaoping Zang ◽  
E. P. Petrov
Keyword(s):  
Dynamic Properties ◽  
Forced Response ◽  
High Mode ◽  
Mode Shapes ◽  
Response Analysis ◽  
Fe Model ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Accurate Analysis ◽  
Bladed Disk

This paper is focused on the analysis of effects of mistuning on the forced response of gas turbine engine bladed disks vibrating in the frequency ranges corresponding to higher modes. For high modes considered here, the blade aerofoils are deformed during vibrations and the blade mode shapes differ significantly from beam mode shapes. A model reduction technique is developed for the computationally efficient and accurate analysis of forced response for bladed disks vibrating in high-frequency ranges. The high-fidelity finite element (FE) model of a tuned bladed disk sector is used to provide primary information about dynamic properties of a bladed disk, and the blade mistuning is modeled by specially defined mistuning matrices. The forced response displacement and stress amplitude levels are studied. The effects of different types of mistuning are examined, and the existence of high amplifications of mistuned forced response levels is shown for high-mode vibrations: in some cases, the resonance peak response of a tuned structure can be lower than out-of-resonance amplitudes of its mistuned counterpart.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Intentional Response Reduction by Harmonic Mistuning of Bladed Disks With Aerodynamic Damping

2018 ◽  
Author(s):  
Sebastian Willeke ◽  
Lukas Schwerdt ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Wave Train ◽  
Wave Mode ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Nodal Diameter ◽  
Aerodynamic Damping ◽  
Mode Pair ◽  
Localized Mode ◽  
Amplitude Level

A harmonic mistuning concept for bladed disks is analyzed in order to intentionally reduce the forced response of specific modes below their tuned amplitude level. By splitting a mode pair associated with a specific nodal diameter pattern, the lightly damped traveling wave mode of the nominally tuned blisk is superposed with its counter-rotating complement. Consequently, a standing wave is formed in which the former wave train benefits from an increase in aerodynamic damping. Unlike previous analyses of randomly perturbed configurations, the mode-specific stabilization is intentionally promoted through adjusting the harmonic content of the mistuning pattern. Through a re-orientation of the localized mode shapes in relation to the discrete blades, the response is additionally attenuated by an amount of up to 7.6 %. The achievable level of amplitude reduction is analytically predicted based on the properties of the tuned system. Furthermore, the required degree of mistuning for a sufficient separation of a mode pair is derived.

Design Methods of Friction Damping at Blade-Disk Joints

2009 ◽  
Author(s):  
Jie Hong ◽  
Lulu Chen ◽  
Yanhong Ma ◽  
Xin Yang
Keyword(s):  
Low Frequency ◽  
Harmonic Balance Method ◽  
Large Error ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Tracking Motion ◽  
Nonlinear Force ◽  
Free Mode

Friction at blade-disk joints is an important source of damping that reduces low frequency resonant amplitudes to acceptable levels in blade-disk assemblies. An effective method is proposed to predict nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints in frequency domain, which syncretizes the excellencies of harmonic balance method, dynamic softness method and tracking motion method. Constrained Mode Shapes are introduced to express the relative motion which occurs at the contact interfaces of blade roots. Compared to using free mode shapes, fewer number of constrained mode shapes is required in order to obtain the accurate resonant response of a system with friction dampers when the contact state is fully stick. It is more efficient to predict the nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints. Based on this method, the effect of Boundary Conditions on the resonant frequencies and forced response levels under different engine rotational speeds is investigated. Large error in the prediction of forced response levels under low engine rotational speed by using traditional methods is found. The effects of preload distribution at blade roots and excitation level are also investigated.

Random Response of Multi-Segment Beam May Exceed Response of Homogeneous Counterparts by Order of Magnitude

2020 ◽  
Vol 20 (13) ◽  
pp. 2041006
Author(s):  
T. Fang ◽  
I. Elishakoff ◽  
C. Jiang
Keyword(s):  
Random Vibration ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Random Response ◽  
Euler Beam ◽  
Mode Method ◽  
Order Of Magnitude ◽  
Engineering Significance ◽  
Normal Mode Method

This paper investigates the dynamic properties of an inhomogeneous, Bernoulli–Euler multi-segment beam composed of different materials. To the best of knowledge of the authors, the problem of random vibrations of beams composing of different chunks of the beams, namely, strong and weak parts, has not been studied in the literature. In this paper, exact solution of the natural frequencies and associated mode shapes of the multi-segment Bernoulli–Euler beam are obtained using Krylov–Duncan functions, followed by free, forced, and random vibration analyses using the normal mode method. Special emphasis is placed on two special configurations of multi-segment beam, namely, the ‘rigid-soft-rigid beam’ (RSR beam) and ‘soft-rigid-soft beam’ (SRS beam) as simplest manifestations of the multi-chunked structures. Some remarkable properties exhibited by the dynamic response of multi-segment beam are demonstrated through this work, which may be of considerable engineering significance, and could not have been anticipated in advance, especially quantitatively.

Dynamic Characteristics of Tsing Ma Suspension Bridge

1996 ◽  
Vol 1541 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Siu Kui Au ◽  
Neil Mickleborough ◽  
Paul N. Roschke
Keyword(s):  
Analytical Solutions ◽  
Bridge Deck ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Quantitative Results ◽  
Suspension Cable ◽  
Bending Modes

Numerical simulation was carried out to determine the dynamic properties of the Tsing Ma Suspension Bridge. Both the structure as a whole and individual subcomponents were modeled. Classical analytical solutions for simplified models from the available literature were compared with the results obtained from a finite-element code. Quantitative results for static deflection, natural frequencies, and mode shapes were compared with analytical solutions from linear theory. Out-of-plane modes were shown to be dominant. For in-plane antisymmetric and symmetric bending modes, in which the suspension cable and bridge deck vibrate in the same direction, the natural frequency of the main span of the bridge is determined to be approximately equal to the square root of the sum of the squares of the frequencies of the cable and bridge deck.

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