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TECHNICAL PAPERS

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

[+] Author and Article Information
E. P. Petrov

Center for Vibration Engineering, Mechanical Engineering Department, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

J. Turbomach 126(1), 175-183 (Mar 26, 2004) (9 pages) doi:10.1115/1.1644558 History: Received December 01, 2002; Revised March 01, 2003; Online March 26, 2004
Copyright © 2004 by ASME
Topics: Force , Vibration , Disks , Equations
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References

Thomas,  D. L., 1979, “Dynamics of Rotationally Periodic Structures,” Int. J. Numer. Methods Eng., 14, pp. 81–102.
Williams,  F. W., 1986, “An Algorithm for Exact Eigenvalue Calculations for Rotationally Periodic Structures,” Int. J. Numer. Methods Eng., 23, pp. 609–622.
Wildheim,  J., 1981, “Vibrations of Rotating Circumferentially Periodic Structures,” Q. J. Mech. Appl. Math., 36, Part 2, pp. 213–229.
Vakakis,  A. F., 1992, “Dynamics of a Nonlinear Periodic Structure With Cyclic Symmetry,” Acta Mech., 95, pp. 197–226.
Samaranayake,  S., and Bajaj,  A. K., 1997, “Subharmonic Oscillations in Harmonically Excited Mechanical Systems With Cyclic Symmetry,” J. Sound Vib., 206(1), pp. 39–60.
Wagner,  L. F., and Griffin,  J. H., 1990, “Blade Vibration With Nonlinear Tip Constraint: Model Development,” ASME J. Turbomach., 112, pp. 778–785.
Csaba,  G., 1998, “Forced Response Analysis in Time and Frequency Domains of a Tuned Bladed Disk With Friction Dampers,” J. Sound Vib., 214(3), pp. 395–412.
Panning, L., Sextro, W., and Popp, K., 2002, “Optimization of the Contact Geometry Between Turbine Blades and Underplatform Dampers With Respect to Friction Damping,” ASME Paper GT-20002-30429.
Yang,  B. D., Chen,  J. J., and Menq,  C. H., 1999, “Prediction of Resonant Response of Shrouded Blades With Three-Dimensional Shroud Constraint,” ASME J. Eng. Gas Turbines Power, 121, pp. 523–529.
Chen, J. J., and Menq, C. H., 1999, “Prediction of Periodic Response of Blades Having 3D Nonlinear Shroud Constraints,” ASME Paper 99-GT-289.
Petrov, E., and Ewins, D., 2002, “Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks With Friction and Impact Dampers,” Proc. of the 7th National Turbine Engine HCF Conference, Universal Technology Corporation, Dayton, OH.
Graham, A., 1981, Kronecker Products and Matrix Calculus With Applications, John Wiley and Sons, New York.
Petrov,  E. P., Sanliturk,  K. Y., and Ewins,  D. J., 2002, “A New Method for Dynamic Analysis of Mistuned Bladed Disks Based on Exact Relationship Between Tuned and Mistuned Systems,” ASME J. Eng. Gas Turbines Power, 122, pp. 586–597.
Petrov, E., and Ewins, D., 2002, “Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks,” ASME Paper GT-20002-30325.
Petrov, E. P., and Ewins, D. J., 2002, “Robust Analysis of Periodic Vibration of Structures With Friction and Gaps Based on Analytical Derivation of Nonlinear Interface Elements,” Proceedings of 5th World Congress on Computational Mechanics, July 7–12, Vienna University of Technology, Vienna, Austria.

Figures

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A cyclically symmetric bladed disk; (a) a whole structure, (b) a sector
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Models of the bladed disk compared: (a) a sector model, (b) the whole structure
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Comparison of results obtained with the proposed method and with using the whole bladed disk model: (a) a case of friction dampers, (b) nonlinear spring elements with nonlinear cubic dependence of forces on displacements, (c) gap elements
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Finite element model: (a) a sector of the bladed disk, (b) shroud of the sector model with shrouds adjacent to it, (c) interface nodes where friction and impact forces are considered
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Natural frequencies of a tuned bladed high-pressure turbine disk and the analyzed frequency range
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Forced response of the bladed disk for excitation by 4EO: (a) a case of different clearance values, (b) a case of different interference values
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Forced response of the bladed disk for excitation of different engine orders: (a) a case with gap between shrouds of 0.01 mm, (b) a case with interferences of 10−6mm

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