Periodic and quasi-periodic solutions for multi-instabilities involved in brake squeal

Journal of Sound and Vibration

Volumn 328, Issue 4-5, 2009, Pages 520-540

  Coudeyras, N ^a,b   Nacivet, S ^b   Sinou, J J ^a  

^a LABORATOIRE DE TRIBOLOGIE ET DYNAMIQUE DES SYSTÈMES   (France)

^b CENTRO RICERCHE FIAT   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

AUTONOMOUS SYSTEMS; BRAKE SQUEAL; COMPLEX EIGENVALUE ANALYSIS; DISC BRAKES; FINITE ELEMENT MODELS; FRICTION COEFFICIENTS; HARMONIC BALANCE METHOD; NON-LINEAR DYNAMICS; NON-LINEAR METHODS; NUMERICAL RESULTS; PERIODIC RESPONSE; QUASI-PERIODIC SOLUTION; STEADY STATE SOLUTION; TIME MARCHING; UNSTABLE MODES;

BRAKES; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; NUMERICAL METHODS;

FRICTION;

EID: 70349871406     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2009.08.017     Document Type: Article

References (25)

1. Kinkaid N., O'Reilly O., and Papadopoulos P. Automotive disc brake squeal. Journal of Sound and Vibration 267 (2003) 105-166
2. Ouyang H., Nack W., Yuan Y., and Chen F. Numerical analysis of automotive disc brake squeal: a review. International Journal of Vehicle Noise and Vibration 1 3/4 (2005) 207-231
3. D. Sinclair, N.-J. Manville, Frictional vibration. Journal of Applied Mechanics (1955) 207-213.
4. R.-T. Spurr, A theory of brake squeal, Proceedings of the Institution of Mechanical Engineers, Vol. 1, 1961-1962, pp. 33-40.
5. Hoffmann N., Fisher M., Allgaier R., and Gaul L. A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations. Mechanics Research Communications 29 (2002) 197-205
6. Sinou J.-J., Thouverez F., and Jezequel L. Methods to reduce non-linear mechanical systems for instability computation. Archives of Computational Methods in Engineering-State of the Art Reviews 11 3 (2004) 257-344
7. Moirot, F., 1998. Etude de la stabilité d'un équilibre en présence de frottement de coulomb, application au crissement des freins à disque, Ph.D. Thesis, Ecole Polytechnique.
8. Ouyang H., Mottershead J., Brookfield D., James S., and Cartmell M. Methodology for the determination of dynamic instabilities in a car disc brake. International Journal of Vehicle Design 23 3 (2000) 241-262
9. Massi F., Baillet L., Giannini O., and Sestieri A. Linear and non-linear numerical approaches. Mechanical Systems and Signal Processing 21 (2007) 2374-2393
10. AbuBakar A., and Ouyang H. Complex eigenvalue analysis and dynamic transient analysis in predicting disc brake squeal. International Journal of Vehicle Noise and Vibration 2 2 (2006) 143-155
11. Lorang X., Foy-Margiocchi F., Nguyen Q., and Gautier P. TGV disc brake squeal. Journal of Sound and Vibration 293 (2006) 735-746
12. Groll G.-V., and Ewins D.-J. The harmonic balance method with arclength continuation in rotor/stator contact problems. Journal of Sound and Vibration 241 2 (2001) 223-233
13. Coudeyras N., Sinou J.-J., and Nacivet S. A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: the CHBM. Journal of Sound and Vibration 319 (2008) 1175-1199
14. Sinou J.-J., Coudeyras N., and Nacivet S. Study of the nonlinear stationary dynamic of single and multi instabilities for disc brake squeal. International Journal of Vehicle Design 51 1-2 (2008) 207-222
15. Craig R.-J., and Bampton M. Coupling of substructures for dynamic analyses. American Institute of Aeronautics and Astronautics-Journal 6 7 (1968) 1313-1319
16. Fritz G., Sinou J.-J., Duffal J.-M., and Jezequel L. Effects of damping on brake squeal coalescence patterns-application on a finite element model. Mechanics Research Communications 34 (2007) 181-190
17. Kim Y.-B., and Choi S.-K. A multiple harmonic balance method for the internal resonant vibration of a non-linear Jeffcot rotor. Journal of Sound and Vibration 208 3 (1997) 745-761
18. F. Schilder, W. Vogt, S. Schreiber, H.-M. Osinga, 2005. Fourier methods for quasi-periodic oscillations, Technical Report, Bristol Centre for Applied Nonlinear Mathematics.
19. Chua L.-O., and Ushida A. Algorithm for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies. IEEE Transactions on Circuits and Systems 28 10 (1981) 953-971
20. Ushida A., and Chua L.-O. Frequency-domain analysis of nonlinear circuits driven by multi-tone signals. IEEE Transactions on Circuits and Systems 31 9 (1984) 766-778
21. Cameron T.M., and Griffin J.H. An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. Journal of Applied Mechanics 56 1 (1989) 149-154
22. Iwan W.-D. A generalization of the concept of equivalent linearization. International Journal of Non-Linear Mechanics 8 (1973) 279-287
23. Iwan W.-D., and Mason Jr. A.-B. Equivalent linearization for systems subjected to non-stationary random excitation. International Journal of Non-Linear Mechanics 15 (1979) 71-82
24. Hanh E., and Chen P. Harmonic balance analysis of general squeeze film damped multidegree-of-freedom rotor bearing systems. Journal of Tribology 116 (1994) 499-507
25. Sinou J.-J., Thouverez F., and Jezequel L. Stability analysis and non-linear behavior of structural systems using the complex non-linear analysis (CNLMA). Computers and Structures 84 (2006) 1891-1905