Free vibration of cantilevered arbitrary triangular Mindlin plates

International Journal of Mechanical Sciences

Volumn 38, Issue 4, 1996, Pages 431-442

  Karunasena, W ^a   Kitipornchai, S ^a   Al Bermani, F G A ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

FREE VIBRATIONS; MINDLIN SHEAR DEFORMATION THEORY; RAYLEIGH-RITZ METHOD;

COMPUTER SIMULATION; NUMERICAL METHODS; PLATES (STRUCTURAL COMPONENTS); POLYNOMIALS; SHEAR DEFORMATION; VIBRATIONS (MECHANICAL);

MECHANICAL PROPERTIES;

EID: 0030126509     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7403(95)00060-7     Document Type: Article

References (28)

1. B. W. Andersen, Vibration of triangular cantilever plates by the Ritz method. J. Appl. Mech. 21(4), 365-376 (1954).
2. H. L. Cox and B. Klein, Fundamental frequencies of clamped triangular plates. J. Acoustical Soc. Amer. 27(2), 266-268 (1955).
3. R. M. Christensen, Vibration of a 45° right angle triangular cantilever plate by a gridwork method. AIAA J. 1(8), 1790-1795 (1963).
4. D. Bucco, J. Mazumdar and G. Sved, Vibration analysis of plates of arbitrary shape - a new approach. J. Sound Vibr. 67(2), 253-262 (1979).
5. J. R. Kuttler and V. G. Sigillito, Upper and lower bounds for frequencies of trapezoidal and triangular plates. J. Sound Vibr. 78(4), 585-590 (1981).
6. S. Mirza and M. Bijlani, Vibration of triangular plates. AIAA J. 21(10), 1472-1475 (1983).
7. D. J. Gorman, A highly accurate analytical solution for free vibration analysis of simply supported right triangular plates. J. Sound Vibr. 89(1), 107-118 (1983).
8. D. J. Gorman, Free vibration analysis of right triangular plates with combinations of clamped-simply supported boundary conditions. J. Sound Vibr. 106(3), 419-431 (1986).
9. D. J. Gorman, A modified superposition method for free vibration analysis of right triangular plates. J. Sound Vibr. 112(1), 173-176 (1987).
10. D. J. Gorman, Accurate free vibration analysis of right triangular plates with one free edge. J. Sound Vibr. 131(1), 115-125 (1989).
11. J. C. Utjes, L. Ercoli, P. A. A. Laura and R. D. Santos, Transverse vibrations of right triangular plates having the hypotenuse free. J. Sound Vibr. 102(3), 445-447 (1985).
12. R. B. Bhat, Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables. J. Sound Vibr. 114(1), 65-71 (1987).
13. P. N. Gustafson, W. F. Stokey and C. F. Zorowski, An experimental study of natural vibrations of cantilevered triangular plates. J. Aeronaut. Sci. 20(May), 331-337 (1953).
14. M. P. Kumaraswamy and V. Cadambe, Experimental study of vibration of cantilevered isosceles triangular plates. J. Sci. Ind. Res. (India) 15B(2), 54-60 (1956).
15. A. W. Leissa, Vibration of Plates (NASA SP-160). Washington, D.C.: Office of Technology Utilization, NASA (1969).
16. A. W. Leissa, Recent research in plate vibrations: classical theory. The Shock and Vibration Digest 9(10), 13-24 (1977).
17. A. W. Leissa, Plate vibration research: 1976-1980: classical theory. The Shock and Vibration Digest 13(9), 11-12 (1981).
18. A. W. Leissa, Recent research in plate vibrations: 1981-1985: Part I, classical theory. The Shock and Vibration Digest 19(2), 11-18 (1987).
19. C. S. Kim and S. M. Dickinson, The free flexural vibration of right triangular isotropic and orthotropic plates. J. Sound Vibr. 141(2), 291-312 (1990).
20. K. Y. Lam, K. M. Liew and S. T. Chow, Free vibration analysis of isotropic and orthotropic triangular plates. Int. J. Mech. Sci. 32(5), 455-464 (1990).
21. C. S. Kim and S. M. Dickinson, The free flexural vibration of isotropic and orthotropic general triangular shaped plates. J. Sound Vibr. 152(3), 383-403 (1992).
22. B. Singh and S. Chakraverty, Transverse vibration of triangular plates using characteristic orthogonal polynomials in two variables. Int. J. Mech. Sci. 34(12), 947-955 (1992).
23. O. G. McGee, A. W. Leissa and C. S. Huang, Vibrations of cantilevered skewed trapezoidal and triangular plates with corner stress singularities. Int. J. Mech. Sci. 34(1), 63-84 (1992).
24. E. Reissner, The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12(June), 69-76 (1945).
25. R. D. Mindlin, Influence of rotary inertia and shear in flexural motion of isotropic elastic plates. J. Appl. Mech. 18(1), 31-38 (1951).
26. S. Kitipornchai, K. M. Liew, Y. Xiang and C. M. Wang, Free vibration of isosceles triangular Mindlin plates. Int. J. Mech. Sci. 35(2), 89-102 (1993).
27. O. G. McGee and T. S. Butalia, Natural vibrations of shear deformable cantilevered skewed trapezoidal and triangular thick plates. Computers and Structures 45(5/6), 1033-1059 (1992).
28. B. J. Garbow, J. M. Boyle, J. J. Dongarra and C. B. Moler, in Matrix Eigensystem Routines: EISPACK Guide Extension, pp. 24-25. Springer-Verlag, New York (1977).