Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates

International Journal of Solids and Structures

Volumn 34, Issue 7, 1997, Pages 819-835

  Shu, C ^a   Du, H ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; BOUNDARY CONDITIONS; MATRIX ALGEBRA; PLATES (STRUCTURAL COMPONENTS); STRUCTURAL ANALYSIS; VIBRATIONS (MECHANICAL);

FREE VIBRATION ANALYSIS; GENERALIZED DIFFERENTIAL QUADRATURE METHOD; WEIGHTING COEFFICIENT MATRICES;

DIFFERENTIAL EQUATIONS;

EID: 0031104258     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(96)00057-1     Document Type: Article

References (24)

1. Bellman, R., Kashef, B. G. and Casti, J. (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of Computer Physics 10, 40-52.
2. Bert, C. W., Jang, S. K. and Striz, A. G. (1988) Two new approximate methods for analyzing free vibration of structural components. AIAA Journal 26, 612-618.
3. 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 30, 1737-1744.
4. Bert, C. W., Wang, X. and Striz, A. G. (1994) Static and free vibrational analysis of beams and plates by differential quadrature method. Acta Mechanica 102, 11-24.
5. Blevins, R. D. (1984) Formulas for Natural Frequency and Mode Shape, Robert E. Krieger, Malabar, Florida.
6. Civan, F. and Sliepcevich, C. M. (1983) Application of differential quadrature to transport processes. Journal of Mathematical Analysis Applied 93, 711-724.
7. Civan, F. and Sliepcevich, C. M. (1984) Differential quadrature for multi-dimensional problems. Journal of Mathematical Analysis Applied 101, 423-443.
8. Du, H., Lim, M. K. and Lin, R. M. (1994) Application of generalized differential quadrature method to structural problems. International Journal of Numerical Methods in Engineering 37, 1881-1896.
9. Du, H., Lim, M. K. and Lin, R. M. (1995) Application of differential quadrature to vibration analysis. Journal of Sound and Vibration 181, 279-293.
10. Jang, S. K., Bert, C. W. and Striz, A. G. (1989) Application of differential quadrature to static analysis of structural components. International Journal of Numerical Methods in Engineering 28, 561-577.
11. Leissa, A. W. (1973) The free vibration of rectangular plates. Journal of Sound and Vibration 31, 257-293.
12. Laura, P. A. A. and Gutierrez, R. H. (1993) Analysis of vibrating Timoshenko beams using the method of differential quadrature. Shock and Vibration, 1, 89-93.
13. Mingle, J. O. (1977) The method of differential quadrature for transient nonlinear diffusion. Journal of Mathematical Analysis Applied 60, 559-569.
14. Quan, J. R. and Chang, C. T. (1989) New insights in solving distributed system equations by the quadrature methods - I. Analysis. Computers and Chemical Engineering 13, 779-788.
15. Shu, C. and Richards, B. E. (1990) High resolution of natural convection in a square cavity by generalized differential quadrature. In Proceedings of 3rd Int. Conf. on Advances in Numer. Methods in Engineering: Theory and Applications, Vol. 2, pp. 978-985. Swansea, U.K.
16. Shu, C. (1991) Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. PhD thesis, University of Glasgow.
17. Shu, C. and Richards, B. E. (1992a) Application of generalized differential quadrature to solve two-dimensional incompressible navier-stokes equations. International Journal of Numerical Methods in Fluids 15, 791-798.
18. Shu, C. and Richards, B. E. (1992b) Parallel simulation of incompressible viscous flows by generalized differential quadrature. Computing Systems in Engineering 3, 271-281.
19. Shu, C. and Du, H. (1997) A generalized approach for implementing general boundary conditions in the GDQ free vibration analysis of plates. International Journal of Solids and Structures 34, 837-846.
20. 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 162, 566-572.
21. Wang, X., Striz, A. G. and Bert, C. W. (1993) Free vibration analysis of annular plates by the DQ method. Journal of Sound and Vibration 164, 173-175.
22. Wang, X., Striz, A. G. and Bert, C. W. (1994) Buckling and vibration analysis of skew plates by the differential quadrature method. AIAA Journal 32, 886-888.
23. Wen, C. and Yu, Y. (1993a) Calculation and analysis of weighting coefficient matrices in differential quadrature method. In Computational Engineering (Edited by Kwak, B. M. and Tanaka, M.), pp. 157-162. Elsevier, Oxford.
24. Wen, C. and Yu, Y. (1993b) Differential quadrature method for high order boundary value problems. In Computational Engineering (Edited by Kwak, B. M. and Tanaka, M.), pp. 163-168. Elsevier, Oxford.