Dynamic stiffness formulation, free vibration and wave motion of helical springs

Journal of Sound and Vibration

Volumn 239, Issue 2, 2001, Pages 297-320

  Lee, J ^a   Thompson, D J ^b  

^a Kookmin University   (South Korea)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ALGORITHMS; BOUNDARY CONDITIONS; NATURAL FREQUENCIES; PARTIAL DIFFERENTIAL EQUATIONS; STIFFNESS MATRIX; VIBRATIONS (MECHANICAL); WAVE PROPAGATION;

TRANSFER MATRIX METHOD; WAVENUMBERS;

HELICAL SPRINGS;

EID: 0035151616     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.2000.3169     Document Type: Article

References (20)

1. LOVE A. E. M. The propagation of waves of elastic displacement along a helical wire. Transactions of the Cambridge Philosophical Society. 18:1899;364-374.
2. TIMOSHENKO S. P. Theory of Elastic Stability. 1936;McGraw Hill, New York and London.
3. WITTRICK W. H. On elastic wave propagation in helical springs. International Journal of Mechanical Sciences. 8:1966;25-47.
4. WAHL A. M. Mechanical Springs. 1963;McGraw Hill, New York.
5. JIANG W., JONES W., WU K., WANG T. Non-linear and linear, static, and dynamic analyses of helical springs. Proceedings of the 30th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Mobile, AL April 1989. 1989;386-395.
6. JIANG W., JONES W. K., WANG T. L., WU K. H. Free vibration of helical springs. Transactions of the ASME. 58:1991;222-228.
7. SINHA S. K., COSTELLO G. A. The numerical solution of the dynamic response of helical springs. International Journal for Numerical Methods in Engineering. 12:1978;949-961.
8. BANERJEE J. R., WILLIAMS F. W. An exact dynamic stiffness matrix for coupled extensional-torsional vibration of structural members. Computers and Structures. 50:1994;161-166.
9. WILLIAMS F. W., HOWSON W. P., BANERJEE J. R. Natural frequencies of members with coupled extension-torsional motion: a physical approach. Journal of Sound and Vibration. 165:1993;373-375.
10. MOTTERSHEAD J. E. Finite elements for dynamical analysis of helical rods. International Journal of Mechanical Sciences. 22:1980;267-283.
11. PEARSON D. The transfer matrix method for the vibration of compressed helical springs. Journal of Mechanical Engineering Science. 24:1982;163-171.
12. YILDIRIM VEBIL. Investigation of parameters affecting free vibration frequency of helical springs. International Journal for Numerical Methods in Engineering. 39:1996;99-114.
13. YILDIRIM V., INCE N. Natural frequencies of helical springs of arbitrary shape. Journal of Sound and Vibration. 204:1997;311-329.
14. YILDIRIM VEBIL. An efficient numerical method for predicting the natural frequencies of cylindrical helical springs. International Journal of Mechanical Sciences. 41:1999;919-939.
15. PEARSON D., WITTRICK W. H. An exact solution for the vibration of helical springs using a Bernoulli-Euler model. International Journal of Mechanical Sciences. 28:1986;83-96.
16. WITTRICK W. H., WILLIAMS F. W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics. 24:1971;263-284.
17. KREYSZIG E. Advanced Engineering Mathematics. 1993;Wiley, New York. p. 471.
18. CESNIK C. E. S., HODGES D. H., SUTYRIN V. G. Cross-sectional analysis of composite beams including large initial twist and curvature effects. AIAA Journal. 34:1996;1913-1920.
19. WARBURTON G. B. The Dynamical Behaviour of Structures. 1976;Pergamon Press, Oxford.
20. Matlab User's Guide. 1992;The Math Works Inc.