Nonlinear transient analysis of moderately thick laminated composite sector plates

Abstract This study presents a simple formulation for the nonlinear dynamic analysis of shear-deformable laminated sector plates made up of cylindrically orthotropic layers. The non-axisymmetric formulation in cylindrical coordinates is discretized in space domain using two-dimensional Chebyshev polynomials. Houbolt time marching is used for temporal discretization. Quadratic extrapolation is used for linearization along with fixed-point iteration for obtaining the results. Several combinations of simply supported, clamped and free edge conditions are considered. Convergence study has been carried out and the results are compared with the results of square plates. Effects of boundary conditions, moduli ratio, lamination scheme, sector angle and annularity on the transient deflection response are plotted graphically. Transient responses are compared for step, saw-tooth and sinusoidal loadings.

[1]  A. R. Sobhani,et al.  Elastic linear and non-linear analysis of fiber-reinforced symmetrically laminated sector Mindlin plate , 2004 .

[2]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

[3]  Zohar Yosibash,et al.  Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method , 2004 .

[4]  H. Tanriöver,et al.  Large deflection analysis of unsymmetrically laminated composite plates: analytical-numerical type approach , 2004 .

[5]  D. Gottlieb,et al.  Collocation methods for the solution of von-Kármán dynamic non-linear plate systems , 2004 .

[6]  Yang Xiang,et al.  Exact Solutions for Vibration of Multi-Span Rectangular Mindlin Plates , 2002 .

[7]  Ahmed A. Khdeir,et al.  Free vibration and buckling of unsymmetric cross-ply laminated plates using a refined theory , 1989 .

[8]  Geoffrey Turvey,et al.  Large deflection analysis of eccentrically stiffened sector plates. , 1998 .

[9]  John C. Houbolt,et al.  A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft , 1950 .

[10]  M. Sathyamoorthy,et al.  Nonlinear Vibration Analysis of Plates: A Review and Survey of Current Developments , 1987 .

[11]  Xing-chun Huang,et al.  Nonlinear vibration and dynamic response of simply supported shear deformable laminated plates on elastic foundations , 2003 .

[12]  G. Yamada,et al.  Plate Vibration Research in Japan , 1987 .

[13]  K. Chandrashekhara,et al.  Geometrically non-linear transient analysis of laminated, doubly curved shells , 1985 .

[14]  Y. Nath,et al.  Chebyshev series solution to non-linear boundary value problems in rectangular domain , 1995 .

[15]  H. B. Sharda,et al.  Stability and vibration of thick laminated composite sector plates , 2005 .

[16]  Manouchehr Salehi,et al.  Large deflection analysis of elastic sector Mindlin plates , 1994 .

[17]  R. Benamar,et al.  THE NON-LINEAR FREE VIBRATION OF FULLY CLAMPED RECTANGULAR PLATES: SECOND NON-LINEAR MODE FOR VARIOUS PLATE ASPECT RATIOS , 1999 .

[18]  C. Chia,et al.  Geometrically Nonlinear Behavior of Composite Plates: A Review , 1988 .

[19]  K. K. Shukla,et al.  NON-LINEAR TRANSIENT ANALYSIS OF MODERATELY THICK LAMINATED COMPOSITE PLATES , 2001 .

[20]  Hui-Shen Shen,et al.  Nonlinear bending of shear deformable laminated plates under transverse and in-plane loads and resting on elastic foundations , 2000 .

[21]  Chuh Mei,et al.  Finite Element Method for Nonlinear Free Vibrations of Composite Plates , 1997 .