Three-dimensional elasticity solutions for free vibrations of circular plates: A polynomials-Ritz analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 175, Issue 1-2, 1999, Pages 189-201

  Liew, K M ^a   Yang, B ^a  

^a University of Southern California ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; ELASTICITY; FREQUENCY RESPONSE; PLATE METAL; POLYNOMIALS; THREE DIMENSIONAL; VIBRATIONS (MECHANICAL);

CIRCULAR PLATES; RITZ METHOD; THREE DIMENSIONAL ELASTICITY SOLUTIONS;

DIFFERENTIAL EQUATIONS;

EID: 0032690274     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00368-5     Document Type: Article

References (21)

1. [1] A.W. Leissa, Vibration of plates, NASA SP-169, Office of Technology Utilization, Washington, 1969.
2. [2] A.W. Leissa, Recent research in plate vibrations: Classical theory, Shock Vib. Dig. 9 (1997) 13-24.
3. [3] A.W. Leissa, Plate vibration research, 1976-1980: Classical theory, Shock Vib. Dig. 13 (1981) 11-22.
4. [4] A.W. Leissa, Recent research in plate vibrations, 1981-1985, Part I: Classical theory, Shock Vib. Dig. 19 (1987) 11-18.
5. [5] K.M. Liew, Y. Xiang and S. Kitipornchai, Research on thick plate vibration: A literature survey, J. Sound Vib. 180 (1995) 163-176.
6. [6] H. Deresiewicz and R.D. Mindlin, Axially symmetric flexural vibrations of a circular disk, J. Appl. Mech. 22 (1955) 86-88.
7. [7] S.S. Rao and A.S. Prasad, Natural frequencies of Mindlin circular plates, J. Appl. Mech. 47 (1980) 652-655.
8. [8] T. Irie, G. Yamada and K. Takagi, Natural frequencies of thick annular plates, J. Appl. Mech. 49 (1982) 633-638.
9. [9] K.M. Liew, Y. Xiang, C.M. Wang and S. Kitipornchai, Flexural vibration of shear deformable circular and annular plates on ring supports, Comput. Methods Appl. Mech. Engrg. 110 (1993) 301-315.
10. [10] S. Srinivas, C.V.J. Rao and A.K. Rao, An exact analysis for free vibration of simply-supported homogeneous and laminated thick rectangular plates, J. Sound Vib. 12 (1970) 187-199.
11. [11] W.H. Wittrick, Analytical three-dimensional elasticity solutions to some plate problems, and some observations on Mindlin's plate theory, Int. J. Solid Struct. 23 (1987) 441-464.
12. [12] K.M. Liew, K.C. Hung and M.K. Lim, Free vibration studies on stress-free three-dimensional elastic solids, J. Appl. Mech. 62 (1995) 159-165.
13. [13] K.M. Liew, K.C. Hung and M.K. Lim, Vibration of stress-free hollow cylinders of arbitrary cross section, J. Appl. Mech. 62 (1995) 718-724.
14. [14] J.R. Hutchinson, Axisymmetric flexural vibrations of a thick free circular plate, J. Appl. Mech. 46 (1979) 139-144.
15. [15] J.R. Hutchinson, Vibrations of thick free circular plates, exact versus approximate solutions, J. Appl. Mech. 51 (1984) 581-585.
16. [16] G.W. McMahon, Experimental study of the vibration of solid, isotropic, elastic cylinder, J. Acoust. Soc. Am. 36 (1964) 85-92.
17. [17] K. Sato, Free flexural vibrations of an elliptical plate with free edge, J. Acoust. Soc. Am. 54 (1973) 547-550.
18. [18] Y. Narita, Natural frequencies of free, orthotropic elliptical plates, J. Sound Vib. 93 (1985) 593-597.
19. [19] A.W. Leissa and Y. Narita, Natural frequencies of simply supported circular plates, J. Sound Vib. 70 (1980) 221-229.
20. [20] C.S. Kim and S.M. Dickinson, On the free, transverse vibration of annular and circular, thin, sectorial plates subject to certain complicating effects, J. Sound Vib. 134 (1989) 407-421.
21. [21] H. Carrington, The frequencies of vibration of flat circular plates fixed at the circumference. Philos. Mag. 46 (1925) 139-144.