On the Interaction of Multiple Traveling Wave Modes in the Flutter Vibrations of Friction-Damped Tuned Bladed Disks

2016 ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Steady State ◽  
Traveling Wave ◽  
Basins Of Attraction ◽  
Unstable Wave ◽  
Stable Limit ◽  
Lumped Mass ◽  
Limit States ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Wave Forms

The aerodynamic interference between the blades of a bladed disk can lead to self-excited vibrations known as flutter. Flutter vibrations can reach considerable levels and are thus of special concern in the design of turbomachines. The vibrations can be saturated in so-called limit cycles by the nonlinear dissipative effects related to dry friction in mechanical joints. For a given mode family of a tuned bladed disk, the flutter stability depends on the interblade phase angle, and often multiple traveling wave forms are unstable. In spite of this, previous investigations indicated that in the steady state, friction-damped flutter vibrations of tuned bladed disks are dominated by a single traveling wave component. In contrast, we demonstrate that, in fact, multiple traveling wave components may interact in the steady state. To this end, a phenomenological model is studied, which possesses one lumped mass per sector, elastic Coulomb friction inter-sector coupling, and two unstable traveling waves forms. Depending on the location of the complex eigenvalues of the linearized system, the steady-state vibrations are shown to be dominated by either of the two unstable wave forms or exhibit considerable contributions of both. Both periodic and quasi-periodic attractor forms are computed using Fourier methods and validated with direct time integration. Moreover, the basins of attraction of the different stable limit states are analyzed in detail. Remarkably, even if a stable, periodic vibration in a certain traveling wave is attained, a sufficiently strong instantaneous perturbation of the same form can give rise to a transient ending in a limit cycle with a different traveling wave character.

On the Interaction of Multiple Traveling Wave Modes in the Flutter Vibrations of Friction-Damped Tuned Bladed Disks

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Steady State ◽  
Traveling Wave ◽  
Initial Conditions ◽  
Limit State ◽  
Experimental Investigations ◽  
Frequency Domain Method ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Theoretical Investigations ◽  
Wave Forms

It is well-known that flutter vibrations of bladed disks can be saturated by dry friction. Previous theoretical investigations indicated that the steady-state, friction-damped flutter vibrations of tuned bladed disks are always dominated by a single traveling wave component, even if multiple traveling wave forms are unstable. This contrasts recent experimental investigations where multiple traveling wave forms were found to participate at steady state. In this paper, we demonstrate that this phenomenon can be explained by nonlinear frictional interblade coupling. To this end, we consider a simple phenomenological model of a bladed disk with frictional intersector coupling and two unstable traveling waves forms. Vibrations occur not only in the form of limit cycle oscillations (periodic) but also in the form of limit torus oscillations (quasi-periodic). It is shown how the limit state depends on the initial conditions, and that the occurrence of multiwave flutter depends on the proximity of the complex eigenvalues of the associated unstable waves. Finally, by computing the limit torus oscillation with a frequency-domain method, we lay the cornerstone for the systematic prediction of friction-saturated flutter vibrations of state-of-the-art bladed disk models.

Comparative Performance of Isotropic and Composite Bladed Disks

1989 ◽  
Author(s):  
P. Seshu ◽  
V. Ramamurti
Keyword(s):  
Steady State ◽  
Shell Element ◽  
Cyclic Symmetry ◽  
Bladed Disks ◽  
Comparative Performance ◽  
Composite Blade ◽  
Bladed Disk ◽  
Plate And Shell ◽  
Representative Model ◽  
Symmetry Method

Abstract Using a 3-noded, multilayered anisotropic triangular plate and shell element combined with cyclic symmetry method, a comparison has been drawn on the steady state as well as free vibration behaviour of isotropic and composite bladed disks, taking into account all the geometric and material complexities. Results are presented for a representative model for three cases – isotropic bladed disk, isotropic disk-composite blade, and composite bladed disk.

Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk

2000 ◽  
Author(s):  
John Judge ◽  
Christophe Pierre ◽  
Oral Mehmed
Keyword(s):  
Experimental Investigation ◽  
Traveling Wave ◽  
Forced Response ◽  
Response Amplitude ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Element Analysis ◽  
Mode Localization ◽  
Bladed Disk ◽  
Out Of Plane

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. The primary aim of the experiment is to gain understanding of the phenomena of mode localization and forced response blade amplitude magnification in bladed disks. A stationary, nominally periodic, twelve-bladed disk with simple geometry is subjected to a traveling-wave, out-of-plane, “engine order” excitation delivered via phase-shifted control signals sent to piezo-electric actuators mounted on the blades. The bladed disk is then mistuned by the addition of small, unequal weights to the blade tips, and it is again subjected to a traveling wave excitation. The experimental data is used to verify analytical predictions about the occurrence of localized mode shapes, increases in forced response amplitude, and changes in resonant frequency due to the presence of mistuning. Very good agreement between experimental measurements and finite element analysis is obtained. The out-of-plane response is compared and contrasted with the previously reported in-plane mode localization behavior of the same test specimen. This work also represents an important extension of previous experimental study by investigating a frequency regime in which modal density is lower but disk-blade interaction is significantly greater.

Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk

2000 ◽  
Vol 123 (4) ◽  
pp. 940-950 ◽  
Author(s):  
J. Judge ◽  
C. Pierre ◽  
O. Mehmed
Keyword(s):  
Experimental Investigation ◽  
Traveling Wave ◽  
Forced Response ◽  
Response Amplitude ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Element Analysis ◽  
Mode Localization ◽  
Bladed Disk ◽  
Out Of Plane

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. The primary aim of the experiment is to gain understanding of the phenomena of mode localization and forced response blade amplitude magnification in bladed disks. A stationary, nominally periodic, 12-bladed disk with simple geometry is subjected to a traveling-wave out-of-plane “engine order” excitation delivered via phase-shifted control signals sent to piezoelectric actuators mounted on the blades. The bladed disk is then mistuned by the addition of small, unequal weights to the blade tips, and it is again subjected to a traveling wave excitation. The experimental data is used to verify analytical predictions about the occurrence of localized mode shapes, increases in forced response amplitude, and changes in resonant frequency due to the presence of mistuning. Very good agreement between experimental measurements and finite element analysis is obtained. The out-of-plane response is compared and contrasted with the previously reported in-plane mode localization behavior of the same test specimen. This work also represents an important extension of previous experimental study by investigating a frequency regime in which modal density is lower but disk-blade interaction is significantly greater.

Reduced-Order Modeling of Bladed Disks With Friction Ring Dampers

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Friction Model ◽  
Contact Friction ◽  
Bladed Disks ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Bladed Disk ◽  
Steady State Responses ◽  
State Responses

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed-disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ringlike substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced-order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector-level calculations and allows precalculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution methods. A model of a bladed disk and damper is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis (TDA) in ansys with the full-order model. It is found that the steady-state responses predicted from the ROMs and the results from ansys are in good agreement, and that the ROMs reduce computation time significantly.

Reduced Order Modeling of Bladed Disks With Friction Ring Dampers

2016 ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Friction Model ◽  
Contact Friction ◽  
Bladed Disks ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Bladed Disk

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ring-like substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector level calculation, and allows pre-calculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution method. A model of a bladed disk and damper, is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis in ANSYS with the full order model.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

scholarly journals Experimental Investigation on a Bladed Disk with Traveling Wave Excitation

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 3966
Author(s):  
Luigi Carassale ◽  
Elena Rizzetto
Keyword(s):  
Data Processing ◽  
Traveling Wave ◽  
Frequency Response Function ◽  
Wave Excitation ◽  
Test Rig ◽  
Real Situation ◽  
Bladed Disk ◽  
Experimental Identification ◽  
Alternative Techniques ◽  
Processing Techniques

Bladed disks are key components of turbomachines and their dynamic behavior is strongly conditioned by their small accidental lack of symmetry referred to as blade mistuning. The experimental identification of mistuned disks is complicated due to several reasons related both to measurement and data processing issues. This paper describes the realization of a test rig designed to investigate the behavior of mistuned disks and develop or validate data processing techniques for system identification. To simplify experiments, using the opposite than in the real situation, the disk is fixed, while the excitation is rotating. The response measured during an experiment carried out in the resonance-crossing condition is used to compare three alternative techniques to estimate the frequency-response function of the disk.

Vibration Suppression of Mistuned Coupled-Blade-Disk Systems Using Piezoelectric Circuitry Network

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Piezoelectric Transducer ◽  
Vibration Suppression ◽  
Structural Vibration ◽  
Bladed Disks ◽  
Disk Model ◽  
Bladed Disk ◽  
Engine Order ◽  
Optimal Network ◽  
Random Mistuning ◽  
Engine Components

For bladed-disk assemblies in turbomachinery, the elements are often exposed to aerodynamic loadings, the so-called engine order excitations. It has been reported that such excitations could cause significant structural vibration. The vibration level could become even more excessive when the bladed disk is mistuned, and may cause fatigue damage to the engine components. To effectively suppress vibration in bladed disks, a piezoelectric transducer networking concept has been explored previously by the authors. While promising, the idea was developed based on a simplified bladed-disk model without considering the disk dynamics. To advance the state of the art, this research further extends the investigation with focus on new circuitry designs for a more sophisticated and realistic system model with the consideration of coupled-blade-disk dynamics. A novel multicircuit piezoelectric transducer network is synthesized and analyzed for multiple-harmonic vibration suppression of bladed disks. An optimal network is derived analytically. The performance of the network for bladed disks with random mistuning is examined through Monte Carlo simulation. The effects of variations (mistuning and detuning) in circuit parameters are also studied. A method to improve the system performance and robustness utilizing negative capacitance is discussed. Finally, experiments are carried out to demonstrate the vibration suppression capability of the proposed piezoelectric circuitry network.

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.

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