In-and out-of-plane vibrations of a rotating plate with frictional contact: Investigations on squeal phenomena

Journal of Applied Mechanics, Transactions ASME

Volumn 76, Issue 4, 2009, Pages 1-15

  Spelsberg Korspeter, Gottfried ^a   Hochlenert, Daniel ^a   Kirillov, Oleg N ^a,b   Hagedorn, Peter ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL TREATMENT; COMPLETE SYSTEM; FRICTIONAL CONTACT; FRICTIONAL FORCES; IN-PLANE; KIRCHHOFF; KIRCHHOFF PLATES; LIMIT CYCLE; MAIN COMPONENT; NEW MODEL; NON-LINEARITY; OUT-OF-PLANE; OUT-OF-PLANE VIBRATIONS; PERTURBATION APPROACH; PLATE VIBRATION; SELF-EXCITED VIBRATIONS; STABILITY BOUNDARIES; THEORY OF ELASTICITY;

DISKS (STRUCTURAL COMPONENTS); FRICTION; ROTATION;

ROTATING DISKS;

EID: 67651214326     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3112734     Document Type: Article

References (32)

1. Lamb, H., and Southwell, R., 1921, "The Vibrations of a Spinning Disk," Proc. R. Soc. London, Ser. A, 99, pp. 272-280.
2. Southwell, R., 1922, "On the Free Transverse Vibrations of a Uniform Circular Disc Clamped at Its Centre; and on the Effects of Rotation," Proc. R. Soc. London, Ser. A, 101, pp. 133-153.
3. Washizu, K., 1974, Variational Methods in Elasticity and Plasticity, Pergamon, New York.
4. Baddour, N., and Zu, J., 2001, "A Revisit of Spinning Disk Models. Part I: Derivation of Equations of Motion," Appl. Math. Model., 25, pp. 541-559.
5. Baddour, N., and Zu, J., 2001, "A Revisit of Spinning Disk Models. Part II: Linear Transverse Vibrations," Appl. Math. Model., 25, pp. 561-578.
6. Moser, F., Fischer, M., and Rumold, W., 2002, "Dreidimensionale Messung von Betriebsschwingformen quietschender Scheibenbremsen," VDI-Ber., 1736, pp. 71-83.
7. Mottershead, J., 1998, "Vibration-and Friction-Induced Instability in Disks," Shock Vib. Dig., 30(1), pp. 14-31.
8. Ono, H., Chen, J., and Bogy, D. B., 1991, "Stability Analysis for the Head-Disk Interface in a Flexible Disk Drive," ASME J. Appl. Mech., 58, pp. 1005-1014.
9. Ouyang, H., and Mottershed, J. E., 2004, "Dynamic Instability of an Elastic Disk Under the Action of a Rotating Friction Couple," ASME J. Appl. Mech., 71, pp. 753-758.
10. Kinkaid, N. M., O'Reilly, O. M., and Papadopoulos, P., 2003, "Automotive Disc Brake Squeal," J. Sound Vib., 267, pp. 105-166.
11. Ibrahim, R. A., 1994, "Friction-Induced Vibration, Chatter, Squeal and Chaos, Part I: Mechanics of Contact and Friction," Appl. Mech. Rev., 47(7), pp. 227-253.
12. Tseng, J. G., and Wickert, J. A., 1998, "Nonconservative Stability of a Friction Loaded Disk," ASME J. Vibr. Acoust., 120, pp. 922-929.
13. Hochlenert, D., Spelsberg-Korspeter, G., and Hagedorn, P., 2007, "Friction Induced Vibrations in Moving Continua and Their Application to Brake Squeal," ASME J. Appl. Mech., 74, pp. 542-549.
14. Kirillov, O. N., and Seyranian, A. P., 2004, "Collapse of the Keldysh Chains and Stability of Continuous Nonconservative Systems," SIAM J. Appl. Math., 64(4), pp. 1383-1407.
15. Seyranian, A. P., and Kliem, W., 2001, "Bifurcations of Eigenvalues of Gyroscopic Systems With Parameters Near Stability Boundaries," ASME J. Appl. Mech., 68, pp. 199-205.
16. Chen, J. S., and Jhu, J. L., 1996, "On the In-Plane Vibration and Stability of a Spinning Annular Disk," J. Sound Vib., 195(4), pp. 585-593.
17. Hagedorn, P., 1986, "Eine Bemerkung zur Momentenimpedanz bei Platten-schwingungen in der Substrukturtechnik," ZAMP, 37, pp. 293-303.
18. Vishik, M. I., and Lyusternik, L. A., 1960, "The Solution of Some Perturbation Problems for Matrices and Selfadjoint or Non-Selfadjoint Differential Equations I," Russ. Math. Surveys, 15, pp. 1-73.
19. Vishik, M. I., and Lyusternik, L. A., 1960, "The Asymptotic Behaviour of Solutions of Linear Differential Equations With Large or Quickly Changing Coefficients and Boundary Conditions," Russ. Math. Surveys, 15, pp. 23-91.
20. Vidoli, S., and Vestroni, F., 2005, "Veering Phenomena in Systems With Gyroscopic Coupling," ASME J. Appl. Mech., 72, pp. 641-647.
21. Leissa, A., 1969, "Vibrations of Plates," NASA, Report No. SP-160.
22. Günther, U., and Kirillov, O. N., 2006, "Krein Space Related Perturbation Theory for MHD ct2-Dynamos and Resonant Unfolding of Diabolical Points," J. Phys. A, 39, pp. 10057-10076.
23. Jearsiripongkul, T., 2005, "Squeal in Floating Caliper Disk Brakes: A Mathematical Model," Ph.D. thesis, Technische Universität Darmstadt, Darmstadt, Germany.
24. Renshaw, A. A., and Mote, C. D., 1992, "Absence of One Nodal Diameter Critical Speed Modes in an Axisymmetric Rotating Disk," Trans. ASME, J. Appl. Mech., 59, pp. 687-688.
25. Chen, J.-S., and Jhu, J.-L., 1996, "In-Plane Response of a Rotating Annular Disk Under Fixed Concentrated Edge Loads," Int. J. Mech. Sci., 38(12), pp. 1285-1293.
26. Hochlenert, D., 2006, "Selbsterregte Schwingungen in Scheibenbremsen: Mathematische Modellbildung und aktive Unterdrückung von Bremsenquietschen," Ph.D. thesis, Technische Universität Darmstadt, Darmstadt, Germany.
27. Kirillov, O., Mailybaev, A., and Seyranian, A., 2005, "Unfolding of Eigenvalue Surfaces Near a Diabolic Point Due to a Complex Perturbation," J. Phys. A, 38(24), pp. 5531-5546.
28. Kirillov, O. N., 2007, "Destabilization Paradox Due to Breaking the Hamil-tonian and Reversible Symmetry," Int. J. Non-Linear Mech., 42(1), pp. 71-87.
29. Merkin, D. R., 1997, Introduction to the Theory of Stability, Springer, New York.
30. Seemann, W., and Wauer, J., 1988, "Vibration of High Speed Disk Rotors," Rotating Machinery Dynamics Proceedings of the Second International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-2).
31. Timoshenko, S., and Goodier, J. N., 1951, Theory of Elasticity, McGraw-Hill, New York.
32. Doedel, E., Pfaffenroth, R., Champneys, A., Fairgrieve, T., Kuznetsov, B. S., and Wang, X., 2001, "AUTO 2000: Continuation and Bifurcation Software for Ordinary Differential Equations (With HomCont)," California Institute of Technology, Technical Report.