A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches

Abstract An accurate and efficient solution procedure based on the two-dimensional elasticity theory for free vibration of arbitrary laminated thick circular deep arches with some combinations of classical boundary conditions is introduced. In order to accurately represent the variation of strain across the thickness, the layerwise theory is used to approximate the displacement components in the radial direction. Employing Hamilton's principle, the discretized form of the equations of motion and the related boundary conditions in the radial direction are obtained. The resulting governing equations are then discretized using the differential quadrature method (DQM). After performing the convergence studies, new results for laminated arches with different set of boundary conditions are developed. Additionally, different values of the arch parameters such as opening angle, thickness-to-length and orthotropy ratios are considered. In all cases, comparisons with the results obtained using the finite element software ‘ABAQUS’ and also with those of the first- and higher-order shear deformation theories available in the literature are performed. Close agreements, especially with those of ABAQUS, are achieved.

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

[2]  A. Leissa,et al.  Vibrations of Planar Curved Beams, Rings, and Arches , 1993 .

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

[4]  B. P. Patel,et al.  Shear flexible field‐consistent curved spline beam element for vibration analysis , 1999 .

[5]  M. S. Qatu,et al.  Vibration of laminated composite arches with deep curvature and arbitrary boundaries , 1993 .

[6]  P.A.A. Laura,et al.  Literature Review : Recent Research On Vibrations of Arch-Type Structures , 1987 .

[7]  Y. P. Tseng,et al.  In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis , 2000 .

[8]  Ghodrat Karami,et al.  A new differential quadrature methodology for beam analysis and the associated differential quadrature element method , 2002 .

[9]  Athol J. Carr,et al.  Generalized finite element analysis of laminated curved beams with constant curvature , 1989 .

[10]  P. Malekzadeh,et al.  A DQEM for vibration of shear deformable nonuniform beams with general boundary conditions , 2003 .

[11]  Ghodrat Karami,et al.  In-plane free vibration analysis of circular arches with varying cross-sections using differential quadrature method , 2004 .

[12]  Mohamad S. Qatu,et al.  Theories and analyses of thin and moderately thick laminated composite curved beams , 1993 .

[13]  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 .

[14]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[15]  P. Malekzadeh,et al.  Large deformation analysis of orthotropic skew plates with nonlinear rotationally restrained edges using DQM , 2007 .

[16]  H. Matsunaga.  Free vibration and stability of laminated composite circular arches subjected to initial axial stress , 2004 .

[17]  G. Karami,et al.  Application of a new differential quadrature methodology for free vibration analysis of plates , 2003 .

[18]  Mohamad S. Qatu,et al.  In-plane vibration of slightly curved laminated composite beams , 1992 .

[19]  C. Bert,et al.  Differential Quadrature Method in Computational Mechanics: A Review , 1996 .

[20]  A. R. Setoodeh,et al.  Large deformation analysis of moderately thick laminated plates on nonlinear elastic foundations by DQM , 2007 .