A Three-Dimensional Layerwise-Differential Quadrature Free Vibration of Thick Skew Laminated Composite Plates

Using the layerwise theory in conjunction with the differential quadrature method (DQM), an accurate and efficient solution procedure for the free vibration analysis of thick skew laminated composite plates is introduced. By employing Hamilton's principle and the layerwise theory, the discretized form of the equations of motion in the thickness direction is obtained. Then, the DQM is used to solve the resulting system of differential equations. The fast rate of convergence and high accuracy of the method is established. Then, some new results for skew laminated plates are presented, which can be used as a benchmark solution for future works.

[1]  Parviz Malekzadeh,et al.  Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT , 2008 .

[2]  M. Banan,et al.  Thermal postbuckling of laminated composite skew plates with temperature-dependent properties , 2011 .

[3]  Ahmed S. Ashour.  The free vibration of symmetrically angle-ply laminated fully clamped skew plates , 2009 .

[4]  W. H. Wittrick.  Analytical, three-dimensional elasticity solutions to some plate problems, and some observations on Mindlin's plate theory , 1987 .

[5]  C. Lim.  Three-dimensional vibration analysis of a cantilevered parallelepiped: Exact and approximate solutions , 1999 .

[6]  Ding Zhou,et al.  3-D vibration analysis of skew thick plates using Chebyshev–Ritz method , 2006 .

[7]  T. Mizusawa,et al.  APPLICATION OF THE SPLINE ELEMENT METHOD TO ANALYZE VIBRATION OF SKEW MINDLIN PLATES WITH VARYING THICKNESS IN ONE DIRECTION , 2001 .

[8]  Umut Topal,et al.  Frequency optimization of laminated skew plates , 2009 .

[9]  Ghodrat Karami,et al.  A solution for the vibration and buckling of composite laminates with elastically restrained edges , 2003 .

[10]  A. Houmat.  Three-dimensional free vibration analysis of plates using the h-p version of the finite element method , 2006 .

[11]  M. Kargarnovin,et al.  Free Vibration Analysis of Symmetrically Laminated Fully Clamped Skew Plates Using Extended Kantorovich Method , 2011 .

[12]  E. Hinton,et al.  Natural frequencies and modes of rhombic mindlin plates , 1980 .

[13]  O. G. McGee,et al.  Three-dimensional free vibrations of thick skewed cantilevered plates , 1991 .

[14]  Parviz Malekzadeh,et al.  Three-dimensional free vibration analysis of thick laminated annular sector plates using a hybrid method , 2009 .

[15]  Ghodrat Karami,et al.  Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM , 2004 .

[16]  Gunay Anlas,et al.  VIBRATION ANALYSIS OF SKEW FIBRE-REINFORCED COMPOSITE LAMINATED PLATES , 2001 .

[17]  Prodyot K. Basu,et al.  Free vibration of skew Mindlin plates by p-version of F.E.M. , 2003 .

[18]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[19]  Ding Zhou,et al.  Three-dimensional vibration analysis of cantilevered skew plates , 2008 .

[20]  P. Malekzadeh,et al.  Dynamic response of thick laminated annular sector plates subjected to moving load , 2010 .

[21]  Simon Wang.  VIBRATION OF THIN SKEW FIBRE REINFORCED COMPOSITE LAMINATES , 1997 .

[22]  Roessler,et al.  Mo , 1878, Angewandte Chemie.

[23]  J. N. Reddy,et al.  A generalization of two-dimensional theories of laminated composite plates† , 1987 .

[24]  M. Tahani,et al.  Hybrid layerwise-differential quadrature transient dynamic analysis of functionally graded axisymmetric cylindrical shells subjected to dynamic pressure , 2011 .

[25]  Yang Xiang,et al.  Vibration Of Thick Skew Plates Based On Mindlin Shear Deformation Plate Theory , 1993 .

[26]  Parviz Malekzadeh,et al.  A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates , 2007 .

[27]  K. M. Liew,et al.  Vibration Characteristics of Simply Supported Thick Skew Plates in Three-Dimensional Setting , 1995 .