Free vibration analysis of thin cylindrical shells by the differential quadrature method

Journal of Pressure Vessel Technology, Transactions of the ASME

Volumn 118, Issue 1, 1996, Pages 1-12

  Bert, C W ^a   Malik, M ^a  

^a University of Oklahoma   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; NATURAL FREQUENCIES; PARTIAL DIFFERENTIAL EQUATIONS; PRESSURE VESSELS; STRUCTURAL ANALYSIS; VIBRATIONS (MECHANICAL);

DIFFERENTIAL QUADRATURE METHOD; DISPLACEMENT COORDINATE; EIGHTH-ORDER SYSTEM; FLUGGE THEORY; FREE-FREE SHELLS; STRUCTURAL MECHANICS;

SHELLS (STRUCTURES);

EID: 0030087062     PISSN: 00949930     EISSN: 15288978     Source Type: Journal    
DOI: 10.1115/1.2842156     Document Type: Article

References (32)

1. Arnold, R. N., and Warburton, G. B., 1953, “The Flexural Vibrations of Thin Cylinders,” Proceedings of the Institution of Mechanical Engineers, Vol. 167, pp. 62-80.
2. Bathe, K-J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ.
3. Bellman, R., and Casti, J., 1971, “Differential Quadrature and Long Term Integration,” Journal of Mathematical Analysis and Applications, Vol. 34, pp. 235-238.
4. Bellman, R., Kashef, B. G., and Casti, J., 1972, “Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Differential Equations,” Journal of Computational Physics, Vol. 10, pp. 40-52.
5. Bert, C. W., Jang, S. K., and Striz, A. G., 1988, “Two New Approximate Methods for Analyzing Free Vibration of Structural Components,” AIAA Journal, Vol. 26, pp. 612-618.
6. Bert, C. W., Jang, S. K., and Striz, A. G., 1989, “Nonlinear Bending Analysis of Orthotropic Rectangular Plates by the Method of Differential Quadrature,” Computational Mechanics, Vol. 5, pp. 217-226.
7. Bert, C. W., Wang, X., and Striz, A. G., 1993, “Differential Quadrature for Static and Free Vibration Analysis of Anisotropic Plates,” International Journal of Solids and Structures, Vol. 30, pp. 1737-1744.
8. Bjbrck, A., and Pereyra, V., 1970, “Solution of Vandermonde System of Equations,” Mathematics of Computation, Vol. 24, pp. 893-903.
9. Cheung, Y. K., 1976, Finite Strip Method in Structural Analysis, Pergamon Press, New York, NY.
10. Civan, F., and Sliepcevich, C. M., 1983, “Application of Differential Quadrature to Transport Processes,” Journal of Mathematical Analysis and Applications, Vol. 93, pp. 206-221.
11. Civan, F., and Sliepcevich, C. M., 1984, “On the Solution of the Thomas-Fermi Equation by Differential Quadrature,” Journal of Computational Physics, Vol. 56, pp. 343-348.
12. Civan, F., and Sliepcevich, C. M., 1986, “Solving Integro-Differential Equations by the Quadrature Method,” Integral Methods in Science and Engineering-86, ed., A. Haji-Shaikh, Hemisphere Publishing Co., New York, NY, pp. 106-113.
13. Flugge, W., 1960, Stresses in Shells, Springer-Verlag, Berlin, Germany. Forsberg, K., 1964, “Influence of Boundary Conditions on the Modal Characteristics of Thin Cylindrical Shells,” AIAA Journal, Vol. 2, pp. 2150-2157.
14. Hamming, R. W., 1973, Numerical Methods for Scientists and Engineers, McGraw-Hill, New York, NY.
15. Hinton, E., and Owen, D. R. J., 1979, An Introduction to Finite Element Computations, Pine-Ridge Press Limited, Swansea, U.K. Huebner, K. H., 1975, The Finite Element Method for Engineers, John Wiley & Sons, New York, NY.
16. Jang, S. K., C. W. Bert, and Striz, A. G., 1989, “Application of Differential Quadrature to Static Analysis of Structural Components,” International Journal for Numerical Methods in Engineering, Vol. 28, pp. 561-577.
17. Koval, L. R., and Cranch, E. T., 1962, “On the Free Vibrations of Thin Cylindrical Shells Subjected to an Initial Static Torques,” Proceedings of the Fourth US National Congress of Applied Mechanics, Vol. 1, pp. 107-117.
18. Leissa, A. W., 1973, Vibration of Shells, NASA SP-288, US Government Printing Office, Washington, D.C.
19. Malik, M., and Bert, C. W., 1994, “Differential Quadrature Solution for Steady State Incompressible and Compressible Lubrication Problems,” ASME Journal ofTribology, Vol. 116, pp. 296-302.
20. Malik, M., Bert, C. W., and Kukreti, A. R., 1993, “Differential Quadrature Solution of Uniformly Loaded Circular Plate Resting on Elastic Half-Space,” Contact Mechanics Computational Techniques, eds., M. H. Aliabadi and C. A. Brebbia, Computational Mechanics Publications, Southampton, UK, pp. 385-396.
21. Malik, M., and Civan, F., 1995, “A Comparative Study of Differential Quadrature and Cubature Methods Vis-a-Vis Some Conventional Techniques in Context of Convection-Diffusion-Reaction Problems,” Chemical Engineering Science, Vol. 50, pp. 531-547.
22. Mingle, J. O., 1973, “Computational Considerations in Nonlinear Diffusion,” International Journal for Numerical Methods in Engineering, Vol. 7, pp. 103-116.
23. Press, W. H., Flannery, S. A., Teukolsky, S. A., and Vetterling, W. T., 1988, Numerical Recipes in C, Cambridge University Press, Cambridge, UK.
24. Quan, J. R., and Chang, C. T., 1989a, “New Insights in Solving Distributed System Equations by the Quadrature Method—I. Analysis,” Computers in Chemical Engineering, Vol. 13, pp. 779-788.
25. Quan, J. R., and Chang, C. T., 1989b, “New Insights in Solving Distributed System Equations by the Quadrature Method—II. Numerical Experiments,” Computers in Chemical Engineering, Vol. 13, pp. 1017-1024.
26. Resnick, B. S., and Dugundji, J., 1966, “Effects of Orthotropy, Boundary Conditions, and Eccentricity on the Vibrations of Cylindrical Shells,” Massachusetts Institute of Technology, Aeroelastic and Structures Research Laboratory, ASRL Technical Report 134-2, NTIS Document AD-648077.
27. Sherbourne, A. N., and Pandey, M. D., 1991, “Differential Quadrature Method in the Buckling Analysis of Beams and Composite Plates,” Computers and Structures, Vol. 40, pp. 903-913.
28. Shu, C, and Richards, B. E., 1992, “Application of Generalized Differential Quadrature to Solve Two-Dimensional Incompressible Navier-Stokes Equations,” International Journal of Numerical Methods in Fluids, Vol. 15, pp. 791-798.
29. Wang, X., and Bert, C. W., 1993, “A New Approach in Applying Differential Quadrature to Static and Free Vibrational Analyses of Beams and Plates,” Journal of Sound and Vibration, Vol. 162, pp. 566-572.
30. Warburton, G. B., 1965, “Vibration of Thin Cylindrical Shells,” Journal of Mechanical Engineering Science, Vol. 7, pp. 399-407.
31. Warburton, G. B., and Higgs, J., 1970, “Natural Frequencies of Thin Cantilever Cylindrical Shells,” Journal of Sound and Vibration, Vol. 11, pp. 335-338.
32. Weingarten, V. I., 1964, “Free Vibration of Thin Cylindrical Shells,” AIAA Journal, Vol. 2, pp. 717-722.