Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 1-3, 2006, Pages 134-146

  Ferreira, A J M ^a   Fasshauer, G E ^b  

^a UNIVERSITY OF PORTO   (Portugal)

^b Illinois Institute of Technology   (United States)

Author keywords

Beams; Free vibrations; Meshless methods; Plates; Pseudospectrals; Radial basis functions

Indexed keywords

BEAMS AND GIRDERS; NATURAL FREQUENCIES; PLATES (STRUCTURAL COMPONENTS); VIBRATIONS (MECHANICAL);

FREE VIBRATIONS; MESHLESS METHODS; PSEUDOSPECTRALS; RADIAL BASIS FUNCTIONS;

STRUCTURAL ANALYSIS;

BEAMS AND GIRDERS; NATURAL FREQUENCIES; PLATES (STRUCTURAL COMPONENTS); STRUCTURAL ANALYSIS; VIBRATIONS (MECHANICAL);

EID: 33846557376     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.02.009     Document Type: Article

References (34)

1. Laura P.A.A., and Gutierrez R.H. Analysis of vibrating Timoshenko beams using the method of differential quadrature. Shock Vib. 1 1 (1993) 89-93
2. Bert C.W., and Malik M. Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev. 49 1 (1996) 1-28
3. Liew K.M., Han J.B., and Xiao Z.M. Vibration analysis of circular Mindlin plates using differential quadrature method. J. Sound Vib. 205 5 (1997) 617-630
4. Liew K.M., Hung K.C., and Lim M.K. Vibration of Mindlin plates using boundary characteristic orthogonal polynomials. J. Sound Vib. 182 1 (1995) 77-90
5. Lee J., and Schultz W.W. Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method. J. Sound Vib. 269 (2004) 609-621
6. Bathe K. Finite Element Procedures in Engineering Analysis (1982), Prentice-Hall, Englewood Cliffs, New Jersey
7. Weaver W., and Johnson P. Structural Dynamics by Finite Elements (1987), Prentice-Hall, Englewood Cliffs, New Jersey
8. Reddy J.N. Introduction to the Finite Element Method (1993), McGraw-Hill, New York
9. Ferreira A.J.M. Free vibration analysis of Timoshenko beams and Mindlin plates by radial basis functions. Int. J. Comput. Meth. 2 1 (2005) 15-31
10. Ferreira A.J.M., Roque C.M.C., and Martins P.A.L.S. Radial basis functions and higher-order theories in the analysis of laminated composite beams and plates. Compos. Struct. 66 (2004) 287-293
11. Ferreira A.J.M. A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Compos. Struct. 59 (2003) 385-392
12. Ferreira A.J.M., Roque C.M.C., and Martins P.A.L.S. Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method. Composites: Part B 34 (2003) 627-636
13. Ferreira A.J.M. Thick composite beam analysis using a global meshless approximation based on radial basis functions. Mech. Adv. Mater. Struct. 10 (2003) 271-284
14. Ferreira A.J.M. Analysis of composite plates using a layerwise deformation theory and multiquadrics discretization. Mech. Adv. Mater. Struct. 12 2 (2005) 99-112
15. Ferreira A.J.M. Polyharmonic (thin-plate) splines in the analysis of composite plates. Int. J. Mech. Sci. 46 (2005) 1549-1569
16. Ferreira A.J.M., Batra R.C., Roque C.M.C., Qian L.F., and Martins P.A.L.S. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos. Struct. 69 (2005) 449-457
17. Driscoll T.A., and Fornberg B. Interpolation in the limit of increasingly flat radial basis functions. Comput. Math. Appl. 43 (2002) 413-422
18. Larsson E., and Fornberg B. Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions. Comput. Math. Appl. 49 (2005) 103-130
19. Schaback R. Multivariate interpolation by polynomials and radial basis functions. Constr. Approx. 21 (2005) 293-317
20. Fasshauer G.E. RBF collocation methods as pseudospectral methods. In: Kassab A., Brebbia C.A., Divo E., and Poljak D. (Eds). Boundary Elements vol. XXVII (2005), WIT Press, Southampton 47-56
21. G.E. Fasshauer, RBF collocation methods and pseudospectral methods, preprint, (2004).
22. R.B. Platte and T.A. Driscoll, Eigenvalue stability of radial basis function discretizations for time-dependent problems, Comput. Math. Appl. (2004), submitted for publication.
23. Fornberg B. A Practical Guide to Pseudospectral Methods (1998), Cambridge University Press
24. Trefethen L.N. Spectral Methods in Matlab (2000), SIAM, Philadelphia, PA
25. Schaback R. On the efficiency of interpolation by radial basis functions. In: Le Méhauté A., Rabut C., and Schumaker L.L. (Eds). Proceedings of Surface fitting and multiresolution methods (1997), Vanderbilt University Press 309-318
26. Rippa S. An algorithm for selecting a good value for the parameter c in radial basis function interpolation. Adv. Comput. Math. 11 (1999) 193-210
27. Cheng A.H.-D., and Cabral J.J.S.P. Direct solution of certain ill-posed boundary value problems by collocation method. In: Kassab A., Brebbia C.A., Divo E., and Poljak D. (Eds). Boundary Elements XXVII (2005), WIT Press, Southampton 35-44
28. Canuto C., Hussaini M.Y., Quateroni A., and Zang T.A. Spectral Methods in Fluid Dynamics (1998), Springer Verlag, Berlin
29. Reddy J.N. Mechanics of laminated composite plates (1997), CRC Press, New York
30. Liew K.M., Huang Y.Q., and Reddy J.N. Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput. Methods Appl. Mech. Engrg. 192 (2003) 2203-2222
31. Dawe D.J., and Roufaeil O.L. Rayleigh-Ritz vibration analysis of Mindlin plates. J. Sound Vib. 69 3 (1980) 345-359
32. Liew K.M., Wang J., Ng T.Y., and Tan M.J. Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method. J. Sound Vib. 276 (2004) 997-1017
33. Hinton E. Numerical methods and software for dynamic analysis of plates and shells (1988), Pineridge Press, Swansea
34. Liew K.M., Xiang Y., and Kitipornchai S. Research on thick plate vibration: a literature survey. J. Sound Vib. 180 1 (1995) 163-176