This paper presents the free vibration analysis of composite thick rectangular plates, based on Reddy’s higher order shear deformation theory (HSDT). The plate theory ensures a zero shear-stress condition at the top and bottom surfaces of the plate and do not requires a shear correction factor. Although the plate theory is quite attractive, it could not be used in the finite element analysis. This is due to the difficulties associated with the satisfaction of the continuity requirement. To overcome this problem associated with Reddy’s HSDT, a new -HSDT p-element with eight degrees of freedom per node is developed and used to find natural frequencies of thick composite plates. The formulation is easily implemented into simple and efficient finite element programs in which the trigonometric hierarchical shape functions are used. A fast convergence and excellent agreement with the known results in the literature are obtained using only one element. Besides, the effects of the boundary conditions, core to face sheet thickness ratio, Young’s modulus ratio on the natural frequencies are investigated through the analysis of these numerical results.
NelsonRBLorchDR. A refined theory for laminated orthotropic plates. ASME J Appl Mech1974; 41: 177–183.
4.
LoKHChristenRMWuEM. A higher order theory of plate deformation – part 1: homogeneous plates. ASME J Appl Mech1979; 44: 663–668.
5.
LevinsonM. An accurate simple theory of the statics and dynamics of elastic plates. Mech Res Commun1980; 7: 343–350.
6.
Murty MVV. An improved transverse shear deformation theory for laminated anistropic plates. NASA Technical Paper 1903, 1981.
7.
ReddyJN. A simple higher-order theory for laminated composite plates. ASME J Appl Mech1984; 51: 745–752.
8.
KantTVaraiyaJHAroraCP. Finite element transient analysis of composite and sandwich plates based a refined theory and implicit time integration schemes. Comput Struct1990; 36: 401–420.
9.
NayakAKMoySSJShenoiRA. Free vibration analysis of composite sandwich plates based on Reddy’s higher order theory. Compos Part B: Eng2002; 33(7): 505–519.
AsadiEFariborzSJ. Free vibration of composite plates with mixed boundary conditions based on higher-order shear deformation theory. Arch Appl Mech2012; 82: 755–766.
12.
BatraRCAimmaneeS. Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories. Comput Struct2005; 83: 934–955.
13.
KapuriaSKulkarniSD. An improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory for static analysis of composite and sandwich plates. J Numer Method Eng2007; 69: 1948–1981.
14.
AmbartsumianSA. On the theory of bending plates. Izv Otd Tech Nauk. AN SSSR1958; 5: 69–77.
15.
SoldatosKPTimarciT. A unified formulation of laminated composites, shear deformable, five-degrees-of-freedom cylindrical shell theories. Compos Struct1993; 25: 165–171.
16.
ReddyJN. Energy and variational methods in applied mechanics, London: Wiley, 1984.
17.
TouratierM. An efficient standard plate theory. Int J Eng Sci1991; 29(8): 901–916.
18.
KaramaMAfaqKSMistouS. Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. Inter J Solids Struct2003; 40(6): 1525–1546.
19.
SoldatosKP. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica1992; 94: 195–200.
20.
AydogduM. Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges. J Compos Struct2006; 40(23): 2143–2155.
21.
SwaminathanKPatilSS. Analytical solutions using a higher order refined computational model with 12 degrees of freedom for the free vibration analysis of antisymmetric angle-ply plates. Compos Struct2008; 82: 209–216.
22.
AydogduM. A new shear deformation theory for laminated composite plates. Compos Struct2009; 89: 94–101.
23.
CarreraE. Theories and finite elements for multilayered plates and shells. A unified compact formulation with numerical assessment and benchmarking. Arch Comput Meth Eng2003; 10: 215–296.
24.
CarreraEBrischettoSA. Survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Appl Mech Rev2008; 62(1): 010803–010803.
25.
BrischettoS. An exact 3D solution for free vibrations of multilayered cross-ply composite and sandwich plates and shells. Int J Appl Mech2014; 6(6): 1450076–1450076.
26.
BrischettoSTorreR. Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders. Curved Layer Struct2014; 1: 59–92.
27.
SzaboBASahrmannGJ. Hierarchical plate and shells models based on p extension. Int J Numer Method Eng1988; 26: 1855–1881.
28.
SzaboBABabuskaI. Finite element analysis, New York: Wiley-lnterscience, 1991.
29.
Hamza-CherifSM. Free vibration analysis of rotating cantilever plates using the p-version of the finite element method. Struct Eng Mech2006; 22: 151–167.
30.
HoumatA. An alternative hierarchical finite element formulation applied to plate vibrations. J Sound Vib1997; 206(2): 201–215.
31.
NosierAKapaniaRKReddyJN. Free vibration analysis of laminated plates using a layerwise theory. AIAA J1993; 31(12): 2335–2346.
32.
MatsunagaH. Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Compos Struct2000; 48: 231–244.
33.
WuCPChenWY. Vibration and stability of laminated plates based on a local high order plate theory. J Sound Vib1994; 177(4): 503–520.
34.
ChoKNBertCWStrizAG. Free vibrations of laminated rectangular plates analyzed by high order individual-layer theory. J Sound Vib1991; 145(3): 429–442.
35.
NatarajanSFerreiraAJMBordasSPA. Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements. Compos Struct2013; 105: 75–81.
OwenDRJLiZH. A refined analysis of laminated plates by finite-element displacement methods -II. Vibration and stability. Comput Struct1987; 26: 915–923.
38.
SunCTLiouWJ. A three-dimensional hybrid stress finite element formulation for free vibrations of laminated composite plates. J Sound Vib1987; 119(1): 1–14.
39.
MallikarjunaKantT. A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches. Compos Struct1993; 23: 293–312.
40.
SenthilnathanNRLimKHLeeKH. Buckling of shear deformable plates. AIAA J1987; 25(9): 1268–1271.
41.
KantTSwaminathanK. Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Compos Struct2001; 53: 73–85.
