Optimisation of the vibrational response of ultrasonic cutting systems

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 70, Issue 5, 2005, Pages 645-656

  Cartmell, M P ^a   Lim, F C N ^b   Cardoni, A ^a   Lucas, M ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b SINGAPORE INSTITUTE OF MANUFACTURING TECHNOLOGY   (Singapore)

Author keywords

Cubic stiffness; Nonlinear response modification; Parametric and autoparametric interactions; Ultrasonic systems

Indexed keywords

FREQUENCY DOMAIN ANALYSIS; MATHEMATICAL MODELS; OPTIMIZATION; OSCILLATORS (MECHANICAL); STIFFNESS; VIBRATIONS (MECHANICAL);

AUTOPARAMETRIC INTERACTION; CUBIC STIFFNESS; NONLINEAR RESPONSE MODIFICATION; PARAMETRIC INTERACTION;

ULTRASONIC CUTTING;

EID: 26844513790     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxh086     Document Type: Article

References (19)

1. Aurelle, N., Guyomar, D., Richard, P., Gonnard, P.&Eyraud, L. (1996) Nonlinear behaviour of an ultrasonic transducer. Ultrasonics, 34, 187-191.
2. Cardoni, A. (2003) Characterising the dynamic response of ultrasonic cutting devices. Ph.D. Thesis, Department of Mechanical Engineering, University of Glasgow.
3. Cardoni, A., Lucas, M., Cartmell, M. P.&Lim, F. C. N. (2003) Nonlinear and parametric vibrations in ultrasonic cutting systems. In Cartmell, M.P. (ed.), The 5th International Conference on Modern Practice in Stress and Vibration Analysis, Glasgow, 9-11 September 2003. Switzerland: Trans Tech Publications.
4. Cole, J. D.&Kevorkian, J. (1963) Uniformly valid asymptotic approximations for certain non-linear differential equations. Proceedings of the International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, pp. 113-120.
5. Frieman, E. A. (1963) On a new method in the theory of irreversible processes. J. Math. Phys., 4, 410-418.
6. Lim, F. C. N. (2003) A preliminary investigation into the effects of nonlinear response modification within coupled oscillators. Ph.D. Thesis, Department of Mechanical Engineering, University of Glasgow.
7. Lim, F. C. N., Cartmell, M. P., Cardoni, A.&Lucas M. (2004) A preliminary investigation into optimising the response of vibrating systems used for ultrasonic cutting. J. Sound Vib., 272, 1047-1069.
8. Lucas, M., Graham, G.&Smith, A. C. (1996) Enhanced vibration control of an ultrasonic cutting process. Ultrasonics, 34, 205-211.
9. Nayfeh, A. H. (1965a) A perturbation method for treating nonlinear oscillation problems. J. Math. Phys., 44, 368-374.
10. Nayfeh, A. H. (1965b) Nonlinear oscillations in a hot electron plasma. Phys. Fluids, 8, 1896-1898.
11. Nayfeh, A. H. (1968) Forced oscillations of the Van der Pol oscillator with delayed amplitude limiting. IEEE Trans. Circuit Theory, 15, 192-200.
12. Nayfeh, A. H. (1973) Perturbation Methods. New York: Wiley.
13. Nayfeh, A. H.&Asfar, K. R. (1986) Response of a bar constrained by a nonlinear spring to a harmonic excitation. J. Sound Vib., 105, 1-15.
14. Nusse, H. E.&Yorke, J. A. (1998) Dynamics: Numerical Explorations, 2nd edn. New York: Springer.
15. Oueini, S. S., Chin, C.-M.&Nayfeh, A. H. (1999) Dynamics of a cubic nonlinear vibration absorber. Nonlinear Dyn., 20, 283-295.
16. Sandri, G. (1965) A new method of expansion in mathematical physics. Nuovo Cimento B, 36, 67-93.
17. Sandri, G. (1967) Uniformization of asymptotic expansions. Nonlinear Partial Differential Equations: A Symposium on Methods of Solutions (W. F. Ames ed.). New York: Academic, pp. 259-277.
18. Sturrock, P. A. (1957) Nonlinear effects in electron plasmas. Proc. R. Soc. Lond. A, 242, 277-299.
19. Sturrock, P. A. (1963) Nonlinear theory of electromagnetic waves in plasmas. Stanford University Microwave Laboratory Report No. 1004.