Nature of stationarity of the natural frequencies at the natural modes in the Rayleigh-Ritz method

Journal of Sound and Vibration

Volumn 203, Issue 2, 1997, Pages 251-263

  Bhat, R B ^a  

^a Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; NATURAL FREQUENCIES; VARIATIONAL TECHNIQUES;

GALERKIN METHOD; RAYLEIGH-RITZ METHOD;

VIBRATIONS (MECHANICAL);

EID: 0031554324     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1996.0874     Document Type: Article

References (20)

1. J. KILLINGBECK and G. H. A. COLE 1971 Mathematical Techniques and Physical Applications. New York: Academic Press.
2. D. T. GREENWOOD 1977 Classical Dynamics. Englewood Cliffs, New Jersey: Prentice-Hall.
3. K. WASHIZU 1968 Variational Methods in Elasticity and Plasticity. Oxford: Pergamon Press.
4. S. S. RAO 1995 Mechanical Vibrations. Reading, MA: Addison Wesley.
5. S. TIMOSHENKO, D. H. YOUNG and W. WEAVER JR 1974 Vibration Problems in Engineering. John Wiley and Sons, New York: Fourth Edition.
6. W. T. THOMSON 1993 Theory of Vibration with Applications. Englewood Cliffs, New Jersey: Prentice Hall.
7. F. BADRAKHAN 1993 Journal of Sound and Vibration 162, 190-194. On the application of Rayleigh's method to an unconstrained system.
8. J. P. DEN HARTOG 1985 Mechanical Vibrations. New York: Dover Publishers.
9. A. W. LEISSA 1973 Journal of Sound and Vibration 31, 257-293. The free vibration of rectangular plates.
10. R. B. BHAT 1996 Journal of Sound and Vibration 189, 407-419. Effect of normal mode contents in assumed deflection shapes in Rayleigh-Ritz method.
11. W. C. HURTY and M. F. RUBINSTEIN 1964 Dynamics of Structures. Englewood Cliffs, New Jersey: Prentice Hall.
12. R. L. BURDEN, J. D. FAIRES and A. C. REYNOLDS 1981 Numerical Analysis. Boston, MA: Prindle, Weber and Schmidt.
13. R. B. BHAT 1985 Journal of Sound and Vibration 102, 493-499. Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method.
14. R. B. BHAT and G. MUNDKUR 1993 Journal of Sound and Vibration 161, 157-171. Vibration of plates using plate characteristic functions obtained by reduction of partial differential equation.
15. C. RAJALINGHAM, R. B. BHAT and G. D. XISTRIS, 1996 Journal of Sound and Vibrations. 193, 497-510. Vibrations of rectangular plates using plate characteristic functions as shape functions in Rayleigh-Ritz method.
16. LORD RAYLEIGH 1984 Theory of Sound. New York: Dover Publications: Second Edition, 1945 re-issue.
17. R. SCHMIDT 1981 Industrial Mathematics 31, 37-46. A variant of the Rayleigh-Ritz method.
18. C. W. BERT 1987 Journal of Sound and Vibration 119, 317-326. Application of a version of the Rayleigh technique to problems of bars, beams, columns, membranes and plates.
19. P. A. A. LAURA, B. VALERGA DE GRECO, J. C. UTJES and R. CARNICER 1988 Journal of Sound and Vibration 120, 587-596. Numerical experiments on free and forced vibrations of beams of non-uniform cross-section.
20. P. A. A. LAURA and V. H. CORTINEZ 1986 American Institute of Chemical Engineers Journal 32, 1025-1026. Optimization of eigenvalues when using the Galerkin method.