Axisymmetric vibration of inhomogeneous clamped circular plates: an unusual closed-form solution

Journal of Sound and Vibration

Volumn 233, Issue 4, 2000, Pages 727-738

  Elishakoff, I ^a  

^a Florida Atlantic University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; BUCKLING; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; ELASTICITY; FINITE ELEMENT METHOD; NATURAL FREQUENCIES; PERTURBATION TECHNIQUES; PLATES (STRUCTURAL COMPONENTS);

INHOMOGENOUS CLAMPED CIRCULAR PLATES; RAYLEIGH-RITZ METHOD;

VIBRATIONS (MECHANICAL);

EID: 0033722154     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1999.2825     Document Type: Article

References (21)

1. CHLADNI E. F. F. Die Akustik. 1803;Leipzig.
2. POISSON S. D. L'Équilibre et le mouvement des corps élastiques. Memories de l'Academie Royales des Sciences de l'Institut de la France. 8:1829;357.
3. GONTKEVICH V. S. Free Vibrations of Plates and Shells. 1964;Naukova Dumka Publishing, Kiev.
4. A. W. LEISSA, 1969, NASA SP 160, Vibration of plates.
5. LEISSA A. W. Plate vibration research: 1976-1980. The Shock and Vibration Digest. 10:1981;19-36.
6. LEISSA A. W. Recent studies in plate vibrations: 1981-85, Part II, complicating effects. The Shock and Vibration Digest. 19:1987;10-24.
7. CONWAY H. D., BECKER E. C. H., DUBIL J. F. Vibration frequencies of tapered bars and circular plates. Journal of Applied Mechanics. 31:1964;329-331.
8. CONVEY H. D. An analogy between the flexural vibrations of a cone and a disc of linearly varying thickness. Zeitschrift fuer angewandte Mathematik und Mechanik. 37:1957;406-407.
9. CONVEY H. D. Some special solutions for flexural vibrations of disc of varying thickness. Ingenieur-Archiv. 26:1958;408-410.
10. SONI S. R. Vibrations of elastic plates and shells of variable thickness. Ph.D. thesis, University of Roorkee. 1972.
11. JAIN R. K. Vibrations of circular plates of variable thickness under an inplane force. Journal of Sound and Vibration. 23:1972;406-414.
12. YANG J. S. The vibration of a circular plate with varying thickness. Journal of Sound and Vibration. 165:1993;178-184.
13. LENOX T. A., CONVEY H. D. An exact, closed-form solution for the flexural vibration of a thin annular plate having a parabolic thickness variation. Journal of Sound and Vibration. 68:1980;231-239.
14. LAURA P. A. A., AVALOS D. R., GALLES C. D. Vibrations and elastic stability of polar orthotropic circular plates of linearly varying thickness. Journal of Sound and Vibration. 82:1982;151-156.
15. LAL R., GUPTA U. S. Axisymmetric vibrations of polar orthotropic annular plates of variable thickness. Journal of Sound and Vibration. 83:1982;229-240.
16. GORMAN D. G. Natural frequencies of transverse vibration of polar orthotropic variable thickness annular plate. Journal of Sound and Vibration. 86:1983;47-60.
17. KANAKA RAJU K. Large amplitude vibrations of circular plates with varying thickness. Journal of Sound and Vibration. 50:1977;399-403.
18. HARRIS C. Z. The normal modes of a circular plate of variable thickness. Quarterly Journal of Mechanics and Applied Mathematics. 21:1968;320-327.
19. CONVEY H. D. An unusual closed-form solution for a variable-thickness plate on an elastic foundation. Journal of Applied Mechanics. 47:1980;204.
20. KOVALENKO A. D. Circular Plates of Variable Thickness. 1959;Naukova Dumka Publishing (in Russia), Kiev.
21. TIMOSHENKO S., WOINOWSKY-KRIEGER S. Theory of Plates and Shells. 1959;McGraw-Hill Book Company, New York.