The differential quadrature method for irregular domains and application to plate vibration

International Journal of Mechanical Sciences

Volumn 38, Issue 6, 1996, Pages 589-606

  Bert, Charles W ^a   Malik, Moinuddin ^a  

^a Univ of Oklahoma   (United States)

Author keywords

Differential quadrature method; Free vibration; Geometric mapping; Irregular domains; Numerical solution methods; Partial differential equations; Thin plate theory

Indexed keywords

BOUNDARY VALUE PROBLEMS; GRAPHIC METHODS; MATHEMATICAL TECHNIQUES; PARTIAL DIFFERENTIAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS); VIBRATIONS (MECHANICAL);

DIFFERENTIAL QUADRATURE METHOD; FREE VIBRATION; GEOMETRIC MAPPING; IRREGULAR DOMAINS; THIN PLATE THEORY;

NUMERICAL METHODS;

EID: 0030174773     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7403(96)80003-8     Document Type: Article

References (32)

1. R. Bellman and J. Casti, Differential quadrature and long term integration. J. Math. Anal. Applic. 34, 235 (1971).
2. R. Bellman, B. G. Kashef and J. Casti, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations. J. Comput. Phys. 10, 40 (1972).
3. F. Civan and C. M. Sliepcevich, Application of differential quadrature to transport processes. J. Math. Anal. Applic. 93, 711 (1983).
4. C. W. Bert, S. K. Jang and A. G. Striz, Two new approximate methods for analyzing free vibration of structural components. AIAA J. 26, 612 (1988).
5. S. K. Jang, C. W. Bert and A. G. Striz, Application of differential quadrature to static analysis of structural components. Int. J. Numer. Meth. Engng 28, 561 (1989).
6. C. W. Bert, X. Wang and A. G. Striz, Differential quadrature for static and free vibration analysis of anisotropic plates. Int. J. Solids Struct. 30, 1737 (1993).
7. C. W. Bert and M. Malik, Free vibration analysis of thin cylindrical shells by the differential quadrature method. ASME J. Press. Vess. Technol. (accepted for publication).
8. M. Malik and C. W. Bert, Differential quadrature solution for steady state incompressible and compressible lubrication problems. ASME J. Trib. 116, 296 (1994).
9. C. W. Bert and M. Malik, Differential quadrature method in computational mechanics: a review. App. Mech. Rev. (accepted for publication).
10. M. Malik and F. Civan, A comparative study of differential quadrature and cubature methods vis-à-vis some conventional techniques in context of convection-diffusion-reaction problems. J. Chem. Engng Sci. 50, 531 (1995).
11. X. Wang, C. W. Bert and A. G. Striz, Buckling and vibration analysis of skew plates by the differential quadrature method. AIAA J. 32, 886 (1994).
12. F. Civan and C. M. Sliepcevich, Application of differential quadrature to solution of pool boiling in cavities. Proc. Okla. Acad. Sci. 65, 73 (1985).
13. A. G. Striz, W. Chen and C. W. Bert, Static analysis of structures by the quadrature element method (QEM). Int. J. Solids Struct. 31, 2807 (1994).
14. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Vol. 1, McGraw-Hill (1989).
15. W. Y. Li, Y. K. Cheung and L. G. Tham, Spline finite strip analysis of general plates. ASCE J. Engng Mech. 112, 43 (1986).
16. Y. K. Cheung, L. G. Tham and W. Y. Li, Free vibration and static analysis of general plates by spline finite strip method. Comput. Mech. 3, 187 (1988).
17. G. N. Geannakakes, Vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in semi-analytical finite strip method. J. Sound Vibr. 137, 282 (1990).
18. 3-spline functions. Int. J. Solids Struct. 31, 657 (1994).
19. F. Civan and C. M. Sliepcevich, Differential quadrature for multi-dimensional problems. J. Math. Anal. Applic. 101, 423 (1984).
20. K.-J. Bathe, Finite Element Procedures in Engineering Analysis. Prentice-Hall (1982).
21. P. S. Nair and S. Durvasula, Vibration of skew plates. J. Sound Vibr. 26, 1 (1973).
22. D. J. Gorman, Accurate free vibration analysis of rhombic plates with simply-supported and fully-clamped edge conditions. J. Sound Vibr. 125, 281 (1988).
23. T. Mizusawa and T. Takami, Vibration of tapered thickness annular sector plates by spline strip method. J. Sound Vibr. 154, 147 (1992).
24. A. W. Leissa, The free vibration of rectangular plates. J. Sound Vibr. 31, 257 (1973).
25. M. Malik and C. W. Bert, Implementing multiple boundary conditions in the DQ solution of higher order differential equations. Int. J. Numer. Meth. Engng (accepted for publication).
26. I. Chopra and S. Durvasula, Vibration of simply-supported trapezoidal plates. J. Sound Vibr. 19, 379 (1971).
27. 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 Vibr. 134, 407 (1989).
28. A. W. Leissa, Vibration of Plates. NASA SP-160, US Government Printing Office, Washington, D.C. (1969).
29. K. Y. Lam, K. M. Liew and S. T. Chow, Use of two-dimensional orthogonal polynomials for vibration analysis of circular and elliptical plates. J Sound Vibr. 154, 261 (1992).
30. B. Singh and S. Chakraverty, On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of transverse vibration of elliptic plates. Comput. Struct. 43, 439 (1992).
31. M. Malik and C. W. Bert, Differential quadratue analysis of free vibration of symmetric cross-ply laminates with shear deformation and rotatory inertia. Shock Vibr. 2, 321 (1995).
32. C. W. Bert and M. Malik, Semi-analytical differential quadrature analysis for free vibration of rectangular plates. AIAA J. (accepted for publication).