Methods based on the differential quadrature in vibration analysis of plates

Journal of Theoretical and Applied Mechanics

Volumn 46, Issue 1, 2008, Pages 123-139

  Krowiak, Artur ^a  

^a CRACOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Differential quadraturemethod; Free vibration; Spline interpolation

Indexed keywords

DIFFERENTIATION (CALCULUS); INTERPOLATION; POLYNOMIALS;

CONVERGENCE AND STABILITY; DIFFERENTIAL QUADRATURE; DIFFERENTIAL QUADRATURE METHODS; DIFFERENTIAL QUADRATUREMETHOD; FREE VIBRATION; FREE-VIBRATION ANALYSIS; INTERPOLATION POLYNOMIALS; SPLINE INTERPOLATION;

VIBRATION ANALYSIS;

EID: 77954987918     PISSN: 14292955     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Bellman R., Casti J., 1971, Differential quadrature and long term integra- tion, Journal of Mathematical Analysis and Application, 34, 235-238
2. Bellman R., Kashef B.G., Casti J., 1972, Differential quadrature: A tech- nique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics, 10, 40-52
3. Bert C.W., Jang S.K., Striz A.G., 1988, Two new methods for analyzing free vibration of structure components, AIAA Journal, 26, 612-6182
4. Bert C.W., Malik M., 1996, Differential quadrature method in computatio- nal mechanics, Applied Mechanics Review, 49, 1-28
5. Bert C.W., Striz A.G., Jang S.K., 1989, Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature, Com- putational Mechanics, 5, 217-226
6. Bert C.W., Wang X., Striz A.G., 1993, Differential quadrature for static and free vibration analysis of anisotropic plates, International Journal of Solid Structures, 30, 1737-1744
7. Feng Y., Bert C.W., 1992, Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam, Nonlinear Dynamics, 3, 13-18
8. Krowiak A., 2006, Symbolic computing in spline-based differential quadrature method, Communications in Numerical Methods in Engineering, 22, 1097-1107
9. Leissa A.W., 1973, The free vibration of rectangular plates, Journal of Sound and Vibration, 31, 257-293
10. Malik M., Civan F., 1994, A comparative study of differential quadratu- re and cubature method vis-á-vis some conventional techniques in context of convection-diffusion-reaction problems, Chemical Engineering Science, 50, 531-547
11. Quan J.R., Chang C.T., 1989, New insight in solving distributed system equations by the quadrature methods I, Computer and Chemical Engineering, 13, 779-788
12. Shu C., 2000, Differential Quadrature and its Application in Engineering, Springer-Verlag, London
13. Shu C., Du H., 1997, Implementation of clamped and simply supported bo- undary conditions in GDQ free vibration analysis of beams and plates, Inter- national Journal of Solids and Structures, 34, 819-835
14. Shu C., Richards B.E., 1992, Application of generalized differential quadra- ture to solve two-dimensional incompressible Nanier-Stokes equations, Interna- tional Journal for Numerical Methods in Fluids, 15, 791-798
15. Wang X., Bert C.W., 1993, A new approach in applying differential quadra- ture to static and free vibration analysis of beams and plates, Journal of Sound and Vibration, 162, 566-572
16. Zhong H., 2004, Spline-based differential quadrature for fourth order diffe- rential equations and its application to Kirchhoff plates, Applied Mathematical Modelling, 28, 353-366