Transverse vibration of a circular plate with unidirectional quadratic thickness variation

International Journal of Mechanical Sciences

Volumn 38, Issue 4, 1996, Pages 423-430

  Singh, Bani ^a   Saxena, Vipin ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; PLATES (STRUCTURAL COMPONENTS); THEORY; VIBRATIONS (MECHANICAL);

FUNDAMENTAL FREQUENCY; RAYLEIGH-RITZ METHOD; TRANSVERSE VIBRATIONS;

MECHANICAL PROPERTIES;

EID: 0030129067     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7403(95)00061-5     Document Type: Article

References (34)

1. A. W. Leissa, Vibration of Plates. NASA SP-160 (1969).
2. W. Soedel, Vibrations of Shells and Plates. Marcel Dekker Inc., New York and Besel (1981).
3. R. Szilard, Theory and Analysis of Plates: Classical and Numerical Methods. Prentice-Hall, Englewood Cliffs, New Jersey (1974).
4. L. Meirovitch, Elements of Vibration Analysis. McGraw-Hill (1986).
5. I. H. Shames and C. L. Dym, Energy and Finite Element Methods in Structural Mechanics. McGraw-Hill (1985).
6. J. Airey, The vibrations of circular plates and their relation to Bessel functions. Proc. Phys. Soc., Lond. 23, 225 (1911).
7. H. Carrington, The frequencies of vibration of flat circular plates fixed at the circumference. Phil. Mag. 50, 1261 (1925).
8. V. S. Gontkevich, Natural Vibrations of Plates and Shells (edited by A.-P. Filipov). Kiev: Nauk Dumka (1964).
9. R. C. Colwell, J. K. Stewart and H. D. Arnett, Symmetric sand figures on circular plates. J. Acoust. Soc. Am. 12, 260 (1940).
10. M. D. Waller, Vibrations of free circular plates. Proc. Phys. Soc., Lond. 50, 70 (1938).
11. N. Cotugno and C. Mengotti-Marzolla, Approssimazione per eccesso della piu bassa frequenza di una piastre ellittrica omogenea incastrata, Atti dell' Accedemia nazionale dei Lincei Memorie 5, Ser. 8, Sem 2 (1943).
12. J. Mazumdar, Transverse vibrations of elastic plates by the method of constant deflection lines. J. Sound Vibr. 18, 147 (1971).
13. R. P. Mcnitt, Free vibrations of a clamped elliptic plate. J. Aerospace Sci. 29, 1124 (1962).
14. Y. Shibaoka, On the transverse vibrations of an elliptic plate with clamped edge. J. Phys. Soc. Japan 11, 797 (1956).
15. G. C. Pardoen, Static vibration and buckling analysis of axisymmetnc circular plates using finite elements. Comput. Struct. 3, 355 (1973).
16. T. Wan, Vibration of circular plates. J. Acoust. Soc. Am. 34, 275 (1962).
17. H. D. Conway, An analogy between the flexural vibrations of a cone and a disc of linearly varying thickness. ZAMM 37, 406 (1957).
18. H. D. Conway, Some special solutions for the flexural vibrations of discs of varying thickness. Ingr. Arch. 26, 408 (1958).
19. B. Singh and V. Saxena, Axisymmetric vibration of a circular plate with double linear variable thickness. J. Sound Vibr. 179, 879 (1995).
20. C. Prasad, R. K. Jain and S. R. Soni, Axisymmetric vibrations of circular plates of linearly varying thickness. ZAMP 23, 941 (1972).
21. S. R. Soni, Vibrations of elastic plates and shells of variable thickness. Ph.D. Thesis, Dept. of Mathematics, U.O.R., Roorkee (1972).
22. B. Singh and R. Goel, Transverse vibrations of an elliptic plate with variable thickness. Proc. Workshop on Solid Mechanics, Dept. of Mathematics, U.O.R. Roorkee, 13-16 March (1985).
23. B. Singh and D. K. Tyagi, Transverse vibrations of an elliptic plate with variable thickness. J. Sound Vibr. 99, 379 (1985).
24. B. Singh and S. Chakraverty. Transverse vibration of Completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method. Int. J. Mech. Sci. 33, 741 (1991).
25. B. Singh and S. Chakraverty, On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of transverse vibration of elliptic plates. Comput. Struct. 43, 439 (1992).
26. B. Singh and S. Chakraverty, Transverse vibration of simply-supported elliptical and circular plates using boundary characteristic orthogonal polyomials in two variables. J. Sound Vibr. 152, 149 (1992).
27. B. Singh and S. Chakraverty, Use of characteristic orthogonal polynomials in two dimensions for transverse vibration of elliptical and circular plates with variable thickness. J. Sound. Vibr. 173, 289 (1994).
28. B. Singh and V. Saxena, Transverse vibration of a clamped circular plate with exponential thickness variation. IX ISME Conf. on Mechanical Engineering., Dept. of Mech. Engng., U.O.R., Roorkee, 10-11 Nov., Vol. II, p. 611 (1994).
29. L. E. Luisoni, P. A. A. Laura and R. O. Grossi, Antisymmetric modes of vibration of a circular plate elastically restrained against rotation and of linearly varying thickness. J. Sound Vibr. 55, 461 (1977).
30. P. A. A. Laura and R. O. Grossi, Influence of Poisson's ratio on the lower natural frequencies of transverse vibration of a circular plate of linearly varying thickness and with an edge elastically restrained against rotation. J. Sound Vibr. 60, 587 (1978).
31. P. A. A. Laura and G. M. Ficcadenti, Transverse vibrations and elastic stability of circular plates of variable thickness and with non-uniform boundary conditions. J. Sound. Vibr. 77, 303 (1981).
32. R. Gelos, G. M. Ficcadenti, R. O. Grossi and P. A. A. Laura, Vibrations of circular plates with variable profile. J. Acoust. Soc. Am. 69, 1326 (1981).
33. D. R. Avalos, P. A. A. Laura and A. M. Bianchi, Analytical and experimental investigation on vibrating circular plates with stepped thickness over a concentric circular region. J. Acoust. Soc. Am. 82, 13 (1987).
34. A. W. Leissa and V. Narita, Natural frequencies of simply-supported circular plates. J. Sound Vibr. 70, 221 (1980).