Ritz analysis of vibrating rectangular and skew multilayered plates based on advanced variable-kinematic models

Composite Structures

Volumn 94, Issue 6, 2012, Pages 2118-2128

  Dozio, Lorenzo ^a   Carrera, Erasmo ^b  

^a POLITECNICO DI MILANO   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Free vibration; Layerwise plate theories; Multilayered plates; Variable kinematic Ritz method

Indexed keywords

CHEBYSHEV POLYNOMIALS; EQUIVALENT SINGLE LAYERS; FREE VIBRATION; FREQUENCY PARAMETERS; HIGHER ORDER; KINEMATIC MODEL; LAYER-WISE; LAYERWISE PLATE THEORIES; MASS MATRICES; MULTILAYERED PLATES; RITZ METHODS; SANDWICH PLATES; SOFT-CORES;

KINEMATICS;

VIBRATIONS (MECHANICAL);

EID: 84859488136     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2012.02.008     Document Type: Article

References (28)

1. Kirchhoff G. über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die reine und angewandte Mathematik 1850, 40:51-88.
2. Mindlin R.D. Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech 1951, 18:1031-1036.
3. Yang P., Norris C.H., Stavsky Y. Elastic propagation in heterogeneous plates. Int J Solids Struct 1966, 2:665-684.
4. Carrera E. Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Methods Eng 2002, 9:87-140.
5. Noor A.K., Burton W.S. Assessment of shear deformation theories for multilayered composite plates. Appl Mech Rev 1989, 41:1-18.
6. Reddy J.N., Robbins D.H. Theories and computational models for composite laminates. Appl Mech Rev 1994, 47:147-165.
7. Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 2003, 56:287-308.
8. Reddy J.N., Arciniega R.A. Shear deformation plate and shell theories: from Stavsky to present. Mech Adv Mater Struct 2004, 11:535-582.
9. Wanji C., Zhen W. A selective review on recent development of displacement-based laminated plate theories. Recent Patents Mech Eng 2008, 1:29-44.
10. Zhang Y.X., Yang C.H. Recent developments in finite element analysis for laminated composite plates. Compos Struct 2009, 88:147-157.
11. Carrera E. A class of two dimensional theories for multilayered plates analysis. Atti Accademia delle Scienze di Torino. Memorie Scienze Fisiche 1995, 1920:49-87.
12. Carrera E. An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates. Compos Struct 2000, 50:183-198.
13. Carrera E., Ciuffreda A. A unified formulation to assess theories of multilayered plates for various bending problems. Compos Struct 2005, 69:271-293.
14. Nali P., Carrera E., Lecca S. Assessments of refined theories for buckling analysis of laminated plates. Compos Struct 2011, 93:456-464.
15. Carrera E., Miglioretti F., Petrolo M. Accuracy of refined finite elements for laminated plate analysis. Compos Struct 2011, 93:1311-1327.
16. Ferreira A.J.M., C Roque C.M., Carrera E., Cinefra M. Analysis of thick isotropic and cross-ply laminated plates by radial basis functions and a unified formulation. J Sound Vib 2011, 330:771-787.
17. Ferreira A.J.M., C Roque C.M., Carrera E., Cinefra M., Polit O. Analysis of laminated plates by trigonometric theory, radial basis, and unified formulation. AIAA J 2011, 49:1559-1562.
18. Dozio L., Carrera E. A variable kinematic Ritz formulation for vibration study of quadrilateral plates with arbitrary thickness. J Sound Vib 2011, 330:4611-4632.
19. Fazzolari F.A., Carrera E. Advanced variable kinematics Ritz and Galerkin formulations for accurate buckling and vibration analysis of anisotropic laminated composite plates. Compos Struct 2011, 94:50-67.
20. Reddy J.N. Mechanics of laminated composite plates and shells 2004, CRC Press.
21. Zhou D., Cheung Y.K., Au F.T.K., Lo S.H. Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method. Int J Solids Struct 2002, 39:6339-6353.
22. Chen W.Q., Lue C.F. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Compos Struct 2005, 69:77-87.
23. Demasi L. Quasi-3D analysis of free vibration of anisotropic plates. Compos Struct 2006, 74:449-457.
24. Garg A.K., Khare R.K., Kant T. Free vibration of skew fiber-reinforced composite and sandwich laminates using a shear deformable finite element method. J Sandwich Struct Mater 2006, 8:33-52.
25. Wang S. Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory. Comput Struct 1997, 63:525-538.
26. Rao M.K., Desai Y.M. Analytical solutions for vibrations of laminated and sandwich plates using mixed theory. Compos Struct 2004, 63:361-373.
27. Frostig Y., Thomsen O.T. Higher-order free vibration of sandwich panels with a flexible core. Int J Solids Struct 2004, 41:1697-1724.
28. Carrera E., Brischetto S. A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Appl Mech Rev 2009, 62:010803-1-010803-17.