Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution

European Journal of Mechanics, A/Solids

Volumn 28, Issue 5, 2009, Pages 991-1013

  Tornabene, Francesco ^a   Viola, Erasmo ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Doubly curved shells; Free vibrations; FSD theory; Functionally graded materials; Generalized Differential Quadrature

Indexed keywords

CERAMIC VOLUME FRACTION; DISCRETIZATION; DOUBLY CURVED SHELLS; DYNAMIC BEHAVIOURS; FIRST-ORDER SHEAR DEFORMATION THEORY; FREE VIBRATION; FREE VIBRATIONS; FSD THEORY; FUNCTIONALLY GRADED; FUNCTIONALLY GRADED SHELL; GENERALIZED DIFFERENTIAL QUADRATURE; GENERALIZED DIFFERENTIAL QUADRATURE METHODS; GOVERNING EQUATIONS OF MOTION; KINEMATIC PARAMETERS; MATERIAL PROFILES; MECHANICAL BEHAVIOUR; MODERATELY THICK; NUMERICAL RESULTS; PARABOLIC SHELLS; POWER LAW DISTRIBUTION; SHELL STRUCTURE; SHELLS OF REVOLUTION; SYSTEM EQUATIONS;

CRACK INITIATION; EQUATIONS OF MOTION; PLATES (STRUCTURAL COMPONENTS); SHEAR DEFORMATION; SHELLS (STRUCTURES);

FUNCTIONALLY GRADED MATERIALS;

EID: 67650753570     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2009.04.005     Document Type: Article

References (32)

1. Abrate S. Free vibration, buckling, and static deflection of functionally graded plates. Compos. Sci. Technol. 66 (2006) 2383-2394
2. Alfano G., Auricchio F., Rosati L., and Sacco E. MITC finite elements for laminated composite plates. Int. J. Numer. Methods Eng. 50 (2001) 707-738
3. Arciniega R.A., and Reddy J.N. Large deformation analysis of functionally graded shells. Int. J. Solids Struct. 44 (2007) 2036-2052
4. Artioli E., Gould P., and Viola E. A differential quadrature method solution for shear-deformable shells of revolution. Eng. Struct. 27 (2005) 1879-1892
5. Artioli E., and Viola E. Static analysis of shear-deformable shells of revolution via G.D.Q. method. Struct. Eng. Mech. 19 (2005) 459-475
6. Artioli E., and Viola E. Free vibration analysis of spherical caps using a G.D.Q. numerical solution. ASME. J. Press Vessel Technol. 128 (2006) 370-378
7. Auricchio F., and Sacco E. A mixed-enhanced finite-element for the analysis of laminated composite plates. Int. J. Numer. Methods Eng. 44 (1999) 1481-1504
8. Auricchio F., and Sacco E. Refined first-order shear deformation theory models for composite laminates. J. Appl. Mech. 70 (2003) 381-390
9. Della Croce L., and Venini P. Finite elements for functionally graded Reissner-Mindlin plates. Comput. Methods Appl. Mech. Eng. 193 (2004) 705-725
10. Elishakoff I., Gentilini C., and Viola E. Forced vibrations of functionally graded plates in the three-dimensional setting. AIAA J. 43 (2005) 2000-2007
11. Elishakoff I., Gentilini C., and Viola E. Three-dimensional analysis of an all-around clamped plate made of functionally graded materials. Acta Mech. 180 (2005) 21-36
12. Liew K.M., He X.Q., and Kitipornchai S. Finite element method for the feedback control of FGM shells in the frequency domain via piezoelectric sensors and actuators. Comput. Methods Appl. Mech. Eng. 193 (2004) 257-273
13. Marzani A., Tornabene F., and Viola E. Nonconservative stability problems via generalized differential quadrature method. J. Sound Vib. 315 (2008) 176-196
14. Ng T.Y., Lam K.Y., and Liew K.M. Effect of FGM materials on the parametric resonance of plate structures. Comput. Methods Appl. Mech. Eng. 190 (2000) 953-962
15. Nie G.J., and Zhong Z. Semi-analytical solution for three dimensional vibration of functionally graded circular plates. Comput. Methods Appl. Mech. Eng. 196 (2007) 4901-4910
16. Patel B.P., Gupta S.S., Loknath M.S., and Kadu C.P. Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory. Compos. Struct. 69 (2005) 259-270
17. Pelletier J.L., and Vel S.S. An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells. Int. J. Solids Struct. 43 (2006) 1131-1158
18. Reddy J.N. Mechanics of Laminated Composites Plates and Shells (2003), CRC Press, New York
19. Roque C.M.C., Ferreira A.J.M., and Jorge R.M.N. A radial basis function for the free vibration analysis of functionally graded plates using refined theory. J. Sound Vib. 300 (2007) 1048-1070
20. Shu C. Differential Quadrature and Its Application in Engineering (2000), Springer, Berlin
21. Toorani M.H., and Lakis A.A. General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects. J. Sound Vib. 237 (2000) 561-615
22. Tornabene, F., 2007. Modellazione e Soluzione di Strutture a Guscio in Materiale Anisotropo. PhD thesis, University of Bologna, DISTART Department.
23. Tornabene F., and Viola E. Vibration analysis of spherical structural elements using the GDQ method. Comput. Math. Appl. 53 (2007) 1538-1560
24. Tornabene F., and Viola E. 2-D solution for free vibrations of parabolic shells using generalized differential quadrature method. Eur. J. Mech. A - Solids 27 (2008) 1001-1025
25. Viola E., and Artioli E. The G.D.Q. method for the harmonic dynamic analysis of rotational shell structural elements. Struct. Eng. Mech. 17 (2004) 789-817
26. Viola E., Dilena M., and Tornabene F. Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches. J. Sound Vib. 299 (2007) 143-163
27. Viola E., and Tornabene F. Vibration analysis of damaged circular arches with varying cross-section. Struct. Integr. Durab. 1 (2005) 155-169 (SID-SDHM)
28. Viola E., and Tornabene F. Vibration analysis of conical shell structures using GDQ method. Far East J. Appl. Math. 25 (2006) 23-39
29. Yang J., Kitipornchai S., and Liew K.M. Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates. Comput. Methods Appl. Mech. Eng. 192 (2003) 3861-3885
30. Yang J., and Shen H.S. Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels. J. Sound Vib. 261 (2007) 871-893
31. Wu C.P., and Tsai Y.H. Asymptotic DQ solutions of functionally graded annular spherical shells. Eur. J. Mech. A - Solids 23 (2004) 283-299
32. Zenkour A.M. Generalized shear deformation theory for bending analysis of functionally graded plates. Appl. Math. Model. 30 (2006) 67-84