Effects of Structural Coupling on Mistuned Cascade Flutter and Response

Kielb, Robert E.; Kaza, K. R. V.

doi:10.1115/1.3239532

Cited by 68 publications

(23 citation statements)

References 3 publications

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“…Qualitatively, these findings are in agreement with the corresponding ones in Ref. 21 where a modified typical section model was used. However, it should be emphasized that the flexibility of the disks which are employed for the current generation of turbofans does not have a significant effect on flutter speed.…”

Section: Flutter Of a Mistuned Bladed-disksupporting

confidence: 92%

Vibration and flutter of mistuned bladed-disk assemblies

Kaza

Kielb

1985

Journal of Propulsion and Power

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An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk is modeled as a circular plate with constant thickness and each blade is represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis are taken to be noncoincident and the structural warping of•the section is explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes is obtained from twodimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes 6'f the blades are included. The equations of motion are derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction are maintained. The equations are solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter.

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Section: Flutter Of a Mistuned Bladed-disksupporting

confidence: 92%

Vibration and flutter of mistuned bladed-disk assemblies

Kaza

Kielb

1985

Journal of Propulsion and Power

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“…The basic flapping and lagging mode shapes for a tuned flexible disk can be described in terms of modal diameters and modal circles. This behavior has also been shown to be true for tuned bladed-disk assemblies (Kielb and Kaza, 1984). The modal diameters vary as cos(nd v), where no is the number of modal diameters and v is the azimuth position around the disk (see Lamb and Southwell, 1921).…”

Section: Bladed Disk Modelmentioning

confidence: 70%

“…For most bladed-disk systems, the level of involuntary mistuning is less than 1 % to 2%. Mistuning may significantly alter the forced response characteristics of bladed-disk systems and, depending on the mistuning pattern, may increase or decrease maximum response levels (Kielb and Kaza, 1984). An important question is the effectiveness of deliberate mistuning in the presence of such involuntary mistuning.…”

Section: Control Strategiesmentioning

confidence: 99%

Vibration Suppression in Bladed-Disk Assemblies With Deliberate Mistuning via Magnetic Bearings

Szasz

Flowers

2000

Journal of Vibration and Control

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This work is a study of bladed-disk vibration control using magnetic bearings. A simulation model consisting of a shaft/bladed-disk assembly supported by two radial magnetic bearings and a thrust bearing is considered. A simplified model is developed and used to identify controllable vibration modes. This information is then used to discuss the potential effectiveness and limitations of bladed-disk vibration control using shaft-based actuators (the magnetic bearings) on symmetric rotors. A control strategy based on using deliberate bladed mistuning is presented for such systems in light of this discussion.

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“…Mistuning may signi cantly alter the forced response characteristics of bladed-disk systems and, depending on the mistuning pattern, may increase or decrease maximum response levels. 12 An important question is the effectiveness of deliberate mistuning in the presence of such involuntary mistuning. From the perspective of this discussion,the worst pattern for involuntary mistuning is one that brings the blade sets closer to a tuned con guration.…”

Section: Controllability and Observabilitymentioning

confidence: 99%

Hub-Based Vibration Control of Multiple Rotating Airfoils

Gy-ograve

Sz-Uuml

et al. 2000

Journal of Propulsion and Power

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A study of vibration control of rotating airfoils using hub-based actuators (speci cally, magnetic bearings) is presented. A simulation model consisting of a shaft/bladed disk assembly supported by two radial magnetic bearings and a thrust bearing is used to investigate the effectiveness and limitationsof such an approach. Aerodynamic effects are accounted for with a simple model, and controllable vibrationmodes are determined. Deliberate patterned blade mistuning is identi ed as a possible strategy to increase system controllability/observability and to improve blade vibration suppression. A measure is developed to quantify relative controllability and observability to evaluate the potential effectiveness of the proposed mistuning strategy. Example simulation results are presented and discussed.= Theodorsen function C 1 = structural damping matrix C 2 = aerodynamic damping matrix c, m = aerodynamic parameters F X 1 = horizontal force at radial bearing one F X 2 = horizontal force at radial bearing two F Y 1 = vertical force at radial bearing one F Y 2 = vertical force at radial bearing two F Z = axial force at thrust bearing I Tbe = tangential inertia of a blade with respect to its endpoint I Th = tangential inertia of hub K C = feedback gain for controller K O = feedback gain for observer K 1 = structural stiffness matrix K 2 = aerodynamic stiffness matrix L s = shaft length between radial bearings l = blade length M 1 = structural mass matrix M 2 = aerodynamic mass matrix m b = mass of a blade m h = mass of hub N = number of blades n = rank of state matrix A O = observability measure P = controllability measure p, q, r = multiblade coordinates R = blade circle radius u = input vector V = freestream air velocity v = row eigenvectors of state matrix A w = column eigenvectors of state matrix A x, y, z = translational degrees of freedom of hub x = state vector x = state vector after multiblade transformation

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Effects of Structural Coupling on Mistuned Cascade Flutter and Response

Cited by 68 publications

References 3 publications

Vibration and flutter of mistuned bladed-disk assemblies

Vibration and flutter of mistuned bladed-disk assemblies

Vibration Suppression in Bladed-Disk Assemblies With Deliberate Mistuning via Magnetic Bearings

Hub-Based Vibration Control of Multiple Rotating Airfoils

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