A method, called the Complex NonLinear Modal Analysis (CNLMA), is proposed for the calculation of the periodic solutions of nonlinear mechanical systems with continued nonlinearities. The equivalent linearization concept and the notion of nonlinear complex modes are applied in order to analyze the steady-state responses of autonomous nonlinear systems. The CNLM-Analysis appears very interesting in regard to computational time; it also necessitates very few computer resources. This method was applied to study instability phenomena in a nonlinear model with a constant brake friction coefficient.
Issue Section:
Technical Papers
1.
Pierre
, C.
, Ferri
, A. A.
, and Dowell
, E. H.
, 1985
, “Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method
,” ASME J. Appl. Mech.
, 52
, pp. 958
–964
.2.
Cameron
, T. M.
, and Griffin
, J. H.
, 1989
, “An Alternating Frequency/Time Domain Method for Calculating the Steady State Response of Nonlinear Dynamic
,” ASME J. Appl. Mech.
, 56
, pp. 149
–154
.3.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley & Sons, New-York.
4.
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods, John Wiley & Sons.
5.
Guckenheimer, J., and Holmes, P., 1986, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag.
6.
Jezequel
, L.
, and Lamarque
, C. H.
, 1991
, “Analysis of Non-linear Dynamical Systems by the Normal Form Theory
,” J. Sound Vib.
, 149
, pp. 429
–459
.7.
Yu
, P.
, 1998
, “Computation of Normal Forms via a Perturbation Technique
,” J. Sound Vib.
, 211
, pp. 19
–38
.8.
Sinou
, J. J.
, Thouverez
, F.
, and Je´ze´quel
, L.
, 2003
, “Center Manifold and Multivariable Approximants Applied to Non-Linear Stability Analysis
,” Int. J. Non-Linear Mech.
, 38/9
, pp. 1421
–1442
.9.
Baker, G. A., and Graves-Morris, P., 1996, Pade´ Approximants, Cambridge University Press, Cambridge.
10.
Brezinski
, C.
, 1983
, “Extrapolation Algorithms and Pade´ Approximations: A Historical Survey
,” Applied Numerical Mathematics
, 20
, pp. 299
–318
.11.
Boudot
, J. P.
, Carneiro
, A.
, and Je´ze´quel
, L.
, 1998
, “Analyze des phe´nome`nes intervenant dans la stabilite´ des syste`mes de freinage. Influence des non-line´arite´s
,” JEF95, Journe´es Europe´ennes de Freinage
, Edition AGIR, Lille, 1
, pp. 213
–224
.12.
Boudot, J. P., 1995, “Mode´lisation des bruits de freinage des ve´hicules Industriels,” The`se de Doctorat, No. 1995-08, Ecole Centrale de Lyon, Ecully.
13.
Sinou, J-J., 2002, “Synthe`se non-line´aire des syste`mes vibrants. Application aux syste`mes de freinage,” The`se de Doctorat, No. 2002-23, Ecole Centrale de Lyon, Ecully.
14.
Rosenberg
, R. M.
, 1962
, “The Normal Modes of Nonlinear n-Degree-of-Freedom Systems
,” ASME J. Appl. Mech.
, 82
, pp. 7
–14
.15.
Rosenberg
, R. M.
, 1966
, “On Non-Linear Vibrations of Systems with Many Degree of Freedom
,” Adv. Appl. Mech.
, 9
, pp. 155
–242
.16.
Szemplinska-Stupinicka
, W.
, 1979
, “The Modified Single Mode Method in the Investigation of the Resonant Vibration of Non-Linear Systems
,” J. Sound Vib.
, 104
(2
), pp. 475
–489
.17.
Szemplinska-Stupinicka, W., 1990, The Behavior of Nonlinear Vibrating Systems, Kluwer Academic.
18.
Shaw
, S. W.
, and Pierre
, C.
, 1993
, “Normal Modes for Non-Linear Vibratory Systems
,” J. Sound Vib.
, 164
(1
), pp. 85
–124
.19.
Iwan
, W. D.
, 1973
, “A Generalization of the Concept of Equivalent Linearization
,” Int. J. Non-Linear Mech.
, 8
, pp. 279
–287
.20.
Ibrahim
, R. A.
, 1994
, “Friction-Induced Vibration, Chatter, Squeal and Chaos: Part II-Dynamics and Modeling
,” ASME J. Appl. Mech.
, 47
(7
), pp. 227
–253
.21.
Oden
, J. T.
, and Martins
, J. A. C.
, 1985
, “Models and Computational Methods for Dynamic friction Phenomena
,” Comput. Methods Appl. Mech. Eng.
, 52
, pp. 527
–634
.22.
Crolla, D. A., and Lang, A. M., “Brake Noise and Vibration-State of Art,” Tribologie Series 18, Vehicle Tribology, Paper VII, pp. 165–174, Dowson, Taylor & Godet, eds., Elsevier.
23.
Spurr
, R. T.
, 1961
–1962, “A Theory of Brake Squeal
,” Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.)
, 1
, pp. 33
–40
.24.
Sridhar
, B.
, and Jordan
, D.
, 1973
, “An Algorithm for Calculation of the Jordan Canonical Form of a Matrix
,” Comput. & Elect. Engng
, 1
, pp. 239
–254
.25.
Bogoliubov, N., and Mitropolski, A., 1961, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York.
26.
Spanos
, P-T. D.
, and Iwan
, W. D.
, 1978
, “On the Existence and Uniqueness of Solutions Generated by Equivalent Linearization
,” Int. J. Non-Linear Mech.
, 13
, pp. 71
–78
.27.
Iwan
, W. D.
, and Patula
, F. J.
, 1972
, “The Merit of Different Minimization Criteria in Approximate Analysis
,” ASME J. Appl. Mech.
, 39
, pp. 257
–262
.28.
Spanos
, P-T. D.
, and Iwan
, W. D.
, 1979
, “Harmonic Analysis of Dynamic Systems with Nonsymmetric Nonlinearities
,” ASME J. Dyn. Syst., Meas., Control
, 101
, pp. 31
–36
.Copyright © 2004
by ASME
You do not currently have access to this content.
