Stability and vibration of mindlin sector plates: An analytical approach

AIAA Journal

Volumn 43, Issue 5, 2005, Pages 1109-1116

  Sharma, Ashish ^a,c   Sharda, H B ^a,c   Nath, Y ^b,d  

^a THAPAR UNIVERSITY   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

^c Mechanical Engineering Department   (India)

^d Applied Mechanics Department

Author keywords

[No Author keywords available]

Indexed keywords

BUCKLING; ELASTIC MODULI; FINITE ELEMENT METHOD; NATURAL FREQUENCIES; REGRESSION ANALYSIS; VIBRATIONS (MECHANICAL);

CHEBYSHEV POLYNOMIALS; MINDLIN SECTOR PLATES; SHEAR CORRECTION FACTORS; SHEAR DEFORMATION THEORY;

PLATES (STRUCTURAL COMPONENTS);

EID: 18944370509     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.4683     Document Type: Article

References (26)

1. Ben-Amoz, M., "Note on Deflections and Flexural Vibrations of Clamped Sectorial Plates," Journal of Applied Mechanics, Vol. 26, No. 1, 1959, pp. 136, 137.
2. Yonezawa, H., "Moments and Free Vibrations in Curved Girder Bridges," Journal of Engineering Mechanics, Vol. 88, No. 1, 1962, pp. 1-21.
3. Ramakrishnan, R., and Kunukkasseril, V. X., "Free Vibration of Annular Sector Plates," Journal of Sound and Vibration, Vol. 30, No. 1, 1973, pp. 127-129.
4. Irie, T., Yamada, G., and Ito, F., "Free Vibration of Polar Orthotropic Sector Plates," Journal of Sound and Vibration, Vol.67, No. 1, 1979, pp. 89-100.
5. Kim, C. S., and Dickinson, S. M., "On the Free Transverse Vibration of Annular and Circular, Thin, Sectorial Plates Subject to Certain Complicating Effects," Journal of Sound and Vibration, Vol. 134, No. 3, 1989, pp. 407-421.
6. Liew, K. M., and Lam, K. Y., "On the Use of 2-D Orthogonal Polynomials in the Rayleigh-Ritz Method For Flexural Vibration of Annular Sector Plates of Arbitrary Shape," International Journal of Mechanical Sciences, Vol. 35, No. 2, 1993, pp. 129-139.
7. Reissner, E., "The Effect of Transverse Shear Deformation on the Bending of Elastic Plates," Journal of Applied Mechanics, Vol. 12, 1945, pp. 69-77.
8. Mindlin, R. D., "Influence of Rotary Inertia and Shear and Shear in Flexural Motion of Isotropic, Elastic Plates," Journal of Applied Mechanics, Vol. 18, 1951, pp. 31-38.
9. Bapu Rao, M. N., Guruswamy, P., and Sampath Kumaran, K. S., "Finite Element Analysis of Thick Annular and Sector Plates," Nuclear Engineering and Design, Vol. 41, No. 2, 1977, pp. 247-255.
10. Guruswamy, P., and Yang, T. Y., "A Sector Element for Dynamic Analysis of Thick Plates," Journal of Sound and Vibration, Vol. 62, No. 3, 1979, pp. 505-516.
11. Srinivasan, R. S., and Thiruvenkatachari, V., "Free Vibration of Transverse Isotropic Annular Sector Mindlin Plates," Journal of Sound and Vibration, Vol. 101, No. 2, 1985, pp. 193-210.
12. Benson, P. R., and Hinton, E., "A Thick Finite Strip Solution for Static, Free Vibration and Stability Problems," International Journal for Numerical Methods in Engineering, Vol. 10, No. 3, 1976, pp. 665-678.
13. Cheung, M. S., and Chan, M. Y. T., "Static and Dynamic Analysis of Thin and Thick Sectorial Plates by the Finite Strip Method," Computers and Structures, Vol. 14, No. 1, 1981, pp. 79-88.
14. Xiang, Y., Liew, K. M., and Kitipornchai, S., "Transverse Vibration of Thick Annular Sector Plates," Journal of the Engineering Mechanics Division, ASCE, Vol. 119, No. 8, 1993, pp. 1579-1599.
15. Ozakca, M., Tay, N., and Kolcu, F., "Buckling Analysis and Shape Optimization of Elastic Variable Thickness Circular and Annular Plates - I. Finite Element Formulation," Engineering Structures, Vol. 25, No. 2, 2003, pp. 181-192.
16. Ozakca, M., Tay, N., and Kolcu, F., "Buckling Analysis and Shape Optimization of Elastic Variable Thickness Circular and Annular Plates - II. Shape Optimization," Engineering Structures, Vol. 25, No. 2, 2003, pp. 193-199.
17. Wang, C. M., Xiang, Y., Kitipornchai, S., and Liew, K. M., "Buckling Solutions of Mindlin Plates of Various Shapes," Engineering Structures, Vol. 16, No. 2, 1994, pp. 119-127.
18. Rubin, C., "Stability of Polar Orthotropic Sector Plates," Journal of Applied Mechanics, Vol. 45, 1978, pp. 448-450.
19. Harik, I. E., "Stability of Annular Sector Plates with Clamped Radial Edges," Journal of Applied Mechanics, Vol. 52, 1985, pp. 971, 972.
20. Wang, C. M., and Xiang, Y., "Deducing Buckling Loads of Sectorial Mindlin Plates from Kirchhoff Plates," Journal of Engineering Mechanics, Vol. 125, No. 5, 1999, pp. 596-598.
21. McGee, O. G., Huang, C. S., and Leissa, A. W., "Comprehensive Exact Solutions for Free Vibrations of Thick Annular Sectorial Plates with Simply Supported Radial Edges," International Journal of Mechanical Sciences, Vol. 37, No. 5, 1995, pp. 537-566.
22. Liew, K. M., and Liu, F.-L., "Differential Quadrature Method for Vibration Analysis of Shear Deformable Annular Sector Plates," Journal of Sound and Vibration, Vol. 230, No. 2, 2000, pp. 335-356.
23. Wilkinson, J. H., and Reinsch, C., Handbook for Automatic Computation, Vol.II - Linear Algebra, Springer-Verlag, New York, 1971.
24. Reddy, J. N., Mechanics of Laminated Composite Plates Theory and Analysis, CRC Press, Boca Raton, FL, 1997.
25. Fox, L., and Parker, I. B., Chebyshev Polynomials in Numerical Analysis, Oxford University Press, London, 1968.
26. Nath, Y., and Kumar, S., "Chebyshev Series Solution of Non-Linear Boundary Value Problem in Rectangular Domain " Computer Methods in Applied Mechanics and Engineering, Vol. 125, Sept. 1995, pp. 41-52.