The study of the dynamic contact in ultrasonic motor

Applied Mathematical Modelling

Volumn 34, Issue 12, 2010, Pages 3767-3777

  Radi, B ^a   El Hami, A ^b  

^a FST Errachidia BP: 509   (Morocco)

^b UNIVERSITÉ ET INSA DE ROUEN   (France)

Author keywords

Augmented Lagrangian; Dynamic contact; Finite element; Normal compliance; Ultrasonic motor

Indexed keywords

AUGMENTED LAGRANGIANS; DYNAMIC CONTACTS; EFFICIENT NUMERICAL METHOD; ELASTIC BODY; FINITE ELEMENT; NORMAL COMPLIANCE; NUMERICAL RESULTS; TIME INTEGRATION ALGORITHMS; ULTRASONIC MOTORS; VARIATIONAL FORMULATION; WEAK SOLUTION;

FAILURE ANALYSIS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; MOTORS; NUMERICAL ANALYSIS; PIEZOELECTRIC DEVICES; PIEZOELECTRIC MOTORS; ROLLING RESISTANCE; ULTRASONIC MACHINE TOOLS; ULTRASONICS;

AUTOMOBILE EXHIBITIONS;

EID: 77954030915     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.03.002     Document Type: Article

References (22)

1. Duvaut G., Lions J.L. Inequalities in Mechanics and Physics 1976, Springer-Verlag, Berlin.
2. Kikuchi N., Oden J.T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Method 1988, Elsevier Science, SIAM, Amsterdam.
3. B. Radi, O.A. Baba, J.C. Gelin, Treatment of the frictional contact via a Lagrangian formulation, Math. Comput. Model., special issue, vol. 28 (4-8) (1998) 407-412.
4. Martins J.A.C., Oden J.T. Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Nonlin. Analysis 1987, 11:407-428.
5. Han W., Sofonea M. Analysis and numerical approximation of an elastic frictional contact problem with normal compliance. Appl. Mathematicae 1999, 26:415-435.
6. Klarbring A., Mikelic̃ A., Shillor M. A global existence results for the quasistatic frictional contact problem with normal compliance. Unilateral Problems in Structural Analysis 1999, vol. 4:85-111. Birkhaäuser, Boston.
7. Rochdi M., Shillor M., Sofonea M. Quasistatic nonlinear viscoelastic contact with normal compliance and friction. J. Elast. 1998, 51:105-126.
8. Le Moal P., Cusin P. Optimization of a traveling wave ultrasonic motors using a three dimensional analysis of the contact mechanism at the stator-rotor interface. Eur. J. Mech. A, Solids 1999, 18:1061-1084.
9. El Hami A., Moro T. Une analyse par la fiabilité des structures des problèmes d'usure du couple stator/rotor dans un moteur piézo-électrique àonde progressive. Revue de la Sreté de Fonctionnement 2003, 24(Tome II):21-34.
10. T. Sashida, T. Kenjo, An Introduction to Ultrasonic Motors, Oxford Science Publications.
11. Sofonea M., Essoufi El-H. A piezoelectric contact problem with slip dependent coefficient of friction. Math. Model. Analy. 2004, 9(3):229-242.
12. Panagiotopoulos P.D. Inequality Problems in Mechanics and Applications 1985, Birkhäuser, Basel.
13. Nec̃as J., Hlavac̃ek I. Mathematical Theory of Elastic and Elastoplastic bodies: An Introduction 1981, Elsevier, Amsterdam.
14. Sofonea M. On a contact problem for elastic-viscoplastic bodies. Nonlin. Anal. TMA 1997, 29:1037-1050.
15. Kavian O. Introduction à la Théorie des Points Critiques et Applications aux Équations Elliptiques 1993, Springer-Verlag, Paris.
16. Barbu V. Semigroups and Differential Equations in Banach Spaces 1976, Nordhoff International Publishing, Leyden, The Netherlands.
17. Baba O.A., Radi B., Gelin J.-C. An augmented Lagrangian treatment of the metal forming process. Math. Comput. Model. 2000, 32(10):171-179.
18. Newmark N.M. A method of computation for structural dynamics. Proceedings of the ASCE. J. Motor. Mech. 1959, 8:67-94.
19. Chung J., Hulbert G.M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-method. J. Appl. Mech. 1993, 60:371-375.
20. A. Czekanski, SA. Meguid, N. El Abbasi, On the selection of a second order accurate integration scheme for elastodynamic contact problems, Special Technical Publications of Engineering Mechanics and Design Laboratory, University of Toronto, vol. STP 168/98-1, pp. 1-28, 1998.
21. Hagedorn P., Wallaschek J. Travelling wave ultrasonic motor. I: Working principle and mathematical modelling of the stator. J. Sound Vib. 1992, 155(1):31-46.
22. Minotti P., Lallement G. Modélisation théorique des moteurs piezoélectriques rotatifs à onde progressive. Mech. Mach. Theory 1994, 29(2):281-292.