A closed form solution for linear and nonlinear free vibrations of composite and fiber metal laminated rectangular plates

Composite Structures

Volumn 92, Issue 11, 2010, Pages 2663-2675

  Shooshtari, A ^a   Razavi, S ^a  

^a BU ALI SINA UNIVERSITY   (Iran)

Author keywords

Composite rectangular plates; Fiber metal laminate; Nonlinear vibration

Indexed keywords

ANALYTICAL RELATIONS; CLOSED FORM SOLUTIONS; COMPATIBILITY EQUATION; FIBER METAL LAMINATES; FIRST-ORDER SHEAR DEFORMATION THEORY; ISOTROPIC RECTANGULAR PLATES; LAMINATED RECTANGULAR PLATES; MULTIPLE TIME SCALE; NON-LINEAR FREE VIBRATION; NON-LINEAR VIBRATIONS; NONLINEAR FREQUENCY; NONLINEAR INERTIA; NONLINEAR ORDINARY DIFFERENTIAL EQUATION; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; RECTANGULAR PLATES; ROTARY INERTIAS; TRANSVERSE DISPLACEMENTS;

BEAMS AND GIRDERS; EQUATIONS OF MOTION; FIBERS; GALERKIN METHODS; LAMINATED COMPOSITES; LAMINATING; METALS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SHEAR DEFORMATION;

NONLINEAR EQUATIONS;

DEFORMATION; FIBER REINFORCED COMPOSITE; LAMINATE; SHEAR PROPERTY; STIFFNESS; STRUCTURAL ANALYSIS; VIBRATION;

EID: 77953356550     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2010.04.001     Document Type: Article

References (43)

1. Harras B., Benamar R., White R.G. Experimental and theoretical investigation of the linear and non-linear dynamic behaviour of a Glare 3 hybrid composite panel. J Sound Vib 2002, 252(2):281-315.
2. Botelho E.C., Campos A.N., de Barros E., Pardini L.C., Rezende M.C. Damping behavior of continuous fiber/metal composite materials by the free vibration method. Compos: Part B 2006, 37:255-263.
3. Botelho E.C., Almeida R.S., Pardini L.C., Rezende M.C. Elastic properties of hygrothermally conditioned glare laminate. Int J Eng Sci 2007, 45:163-172.
4. Malik M., Bert Charles.W. Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method. Int J Solids Struct 1998, 35(3-4):299-318.
5. Ganapathi M., Machetes D.P. Free vibration analysis of multi-layered composite laminates based on an accurate higher-order theory. Compos: Part B 2001, 32:535-543.
6. Liew K.M., Huang Y.Q., Reddy J.N. Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput Methods Appl Mech Eng 2003, 192:2203-2222.
7. Lanhe W., Hua L., Daobin W. Vibration analysis of generally laminated composite plates by the moving least squares differential quadrature method. Compos Struct 2005, 68:319-330.
8. Akhras G., Li W. Static and free vibration analysis of composite plates using spline finite strips with higher-order shear deformation. Compos: Part B 2005, 36:496-503.
9. Xiang S., Wang K.M. Free vibration analysis of symmetric laminated composite plates by trigonometric shear deformation theory and inverse multiquadric RBF. Thin-Walled Struct 2009, 47:304-310.
10. Zhen W., Wanji Chen Free vibration of laminated composite and sandwich plates using global-local higher-order theory. J Sound Vib 2006, 298:333-349.
11. Liu G.R., Zhao X., Dai K.Y., Zhong Z.H., Li G.Y., Han X. Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method. Compos Sci Technol 2008, 68:354-366.
12. Ćetković M., Vuksanović Dj. Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model. Compos Struct 2009, 88:219-227.
13. Zhen W., Cheung Y.K., Lo S.H., Wanji Chen Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plates. Compos Struct 2008, 82:277-289.
14. Attia O., El-Zafrany A. A high-order shear element for nonlinear vibration analysis of composite layered plates and shells. Int J Mech Sci 1999, 41:461-486.
15. Cheng Q.H., Lok T.S., Xie Z.C. Geometrically non-linear analysis including shear deformation of composite laminates. Thin-Walled Struct 1999, 35:41-59.
16. Singh A.V. Linear and geometrically nonlinear vibrations of fiber reinforced laminated plates and shallow shell. Comput Struct 2000, 76:277-285.
17. Andrianov I.V., Danishevs'kyy V.V., Awrejcewicz J. An artificial small perturbation parameter and nonlinear plate vibrations. J Sound Vib 2005, 283:561-571.
18. Li J.-J., Cheng C.-J. Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect. J Sound Vib 2005, 281:295-309.
19. Saha K.N., Misra D., Ghosal S., Pohit G. Nonlinear free vibration analysis of square plates with various boundary conditions. J Sound Vib 2005, 287:1031-1044.
20. Wu W.X., Shu C., Wang C.M. Mesh-free least-squares-based finite difference method for large-amplitude free vibration analysis of arbitrarily shaped thin plates. J Sound Vib 2008, 317:955-974.
21. Singha M.K., Daripa Rupesh Nonlinear vibration and dynamic stability analysis of composite plates. J Sound Vib 2009, 328:541-554.
22. Harras B., Benamar R., White R.G. Geometrically non-linear free vibration of fully clamped symmetrically laminated rectangular composite plates. J Sound Vib 2002, 251(4):579-619.
23. Harras B., Benamar R., White R.G. Investigation of non-linear free vibrations of fully clamped symmetrically laminated carbon-fibre-reinforced PEEK (AS4/APC2) rectangular composite panels. Compos Sci Technol 2002, 62:719-727.
24. Han W., Petyt M. Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method-I: The fundamental mode of isotropic plates. Comput Struct 1997, 63(2):295-308.
25. Han W., Petyt M. Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method-II: 1st mode of laminated plates and higher modes of isotropic and laminated plates. Comput Struct 1997, 63(2):309-318.
26. Ribeiro P., Petyt M. Nonlinear vibration of composite laminated plates by the hierarchical finite element method. Compos Struct 1999, 46:197-208.
27. Ribeiro P., Petyt M. Nonlinear vibration of plates by the hierarchical finite element and continuation methods. Int J Mech Sci 1999, 41:437-459.
28. Ribeiro P. Non-linear forced vibrations of thin/thick beams and plates by the finite element and shooting methods. Comput Struct 2004, 82:1413-1423.
29. Ribeiro P. Forced periodic vibrations of laminated composite plates by a p-version, first order shear deformation, finite element. Compos Sci Technol 2006, 66:1844-1856.
30. Ribeiro P., Duarte R.P. From periodic to chaotic oscillations in composite laminated plates. Comput Struct 2006, 84:1629-1639.
31. Han W., Petyt M., Hsiao Kuo-Mo An investigation into geometrically nonlinear analysis of rectangular laminated plates using the hierarchical finite element method. Finite Elem Anal Des 1994, 18:273-288.
32. Ribeiro P. Nonlinear vibrations of simply-supported plates by the p-version finite element method. Finite Elem Anal Des 2005, 41:911-924.
33. Taazount M., Zinai A., Bouazzouni A. Large free vibration of thin plates: Hierarchic finite Element Method and asymptotic linearization. Euro J Mech A/Solids 2009, 28:155-165.
34. Reddy J.N. Mechanics of laminated composite plates and shells: theory and analysis 2004, CRC Press. second ed.
35. Chia C.Y. Nonlinear Analysis of Plates 1980, McGraw-Hill.
36. Nayfeh A.H., Dean T.Mook. Nonlinear Oscillation 1995, John Wiley & Sons, Inc.
37. Ribeiro P. On the influence of membrane inertia and shear deformation on the geometrically nonlinear vibrations of open, cylindrical, laminated clamped shells. Compos Sci Technol 2009, 69:176-185.
38. Zhang Y., Wang Simon, Loughlan Joe Free vibration analysis of rectangular composite laminates using a layerwise cubic B-spline finite strip method. Thin-Walled Struct 2006, 44:601-622.
39. Botelho E.C., Silva R.A., Pardini L.C., Rezende M.C. A review on the development and properties of continuous fiber/epoxy/aluminum hybrid composites for aircraft structures. Mater Res 2006, 9(3):247-256.
40. Ugural Ansel C. Stresses in Plates and Shells 1999, WCB/McGraw-Hill. second ed.
41. Lu H.X., Li J.Y. Analysis of an initially stressed laminated plate based on elasticity theory. Compos Struct 2009, 88:271-279.
42. Civalek Ö. Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method. Finite Elem Anal Des 2008, 44:725-731.
43. Matsunaga H. Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Compos Struct 2000, 48:231-244.