Vibrations of unsymmetrically laminated plates analyzed by using a higher order theory with a C° finite element formulation

Recently developed shear deformation theory is used to analyze vibrations of laminated composite and sandwich plates in conjunction with a C° isoparametric finite element formulation. The present theory is based on a higher order displacement model and the three-dimensional Hooke's laws for plate material, giving rise to a more realistic representation of the cross-sectional deformation. The theory does not require the usual shear correction coefficients generally associated with Reissner-Mindlin theories. A special mass lumping procedure is used in the dynamic equilibrium equations. The numerical examples presented are compared with 3-D elasticity/analytical and Mindlin's plate solutions, and it is demonstrated that the present model predicts the frequencies more accurately when compared with the first order shear deformation theories and classical plate theories.

[1]  A. K. Rath,et al.  Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Panels , 1975 .

[2]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

[3]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[4]  J. N. Reddy,et al.  Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory , 1986 .

[5]  S. Srinivas,et al.  An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates , 1970 .

[6]  Tarun Kant,et al.  A refined higher-order generally orthotropic C0 plate bending element , 1988 .

[7]  J. N. Reddy,et al.  Free vibration of antisymmetric, angle-ply laminated plates including transverse shear deformation by the finite element method , 1979 .

[8]  O. C. Zienkiewicz,et al.  A refined higher-order C° plate bending element , 1982 .

[9]  Tarun Kant,et al.  Flexural analysis of laminated composites using refined higher-order C ° plate bending elements , 1988 .

[10]  C. Sun,et al.  A higher order theory for extensional motion of laminated composites , 1973 .

[11]  A. Rao,et al.  Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates , 1970 .

[12]  Tarun Kant,et al.  DYNAMICS OF LAMINATED COMPOSITE PLATES WITH A HIGHER ORDER THEORY AND FINITE ELEMENT DISCRETIZATION , 1988 .

[13]  R. Fortier,et al.  On the Vibration of Shear Deformable Curved Anisotropic Composite Plates , 1973 .

[14]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[15]  J. Reddy,et al.  Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory , 1985 .

[16]  Tarun Kant,et al.  Numerical analysis of thick plates , 1982 .

[17]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[18]  A. Gupta,et al.  A method of computing numerically integrated stiffness matrices , 1972 .

[19]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[20]  David R. Owen,et al.  A refined analysis of laminated plates by finite element displacement methods—II. Vibration and stability , 1987 .

[21]  Tarun Kant,et al.  Free vibration of symmetrically laminated plates using a higher‐order theory with finite element technique , 1989 .

[22]  Charles W. Bert,et al.  Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates , 1978 .

[23]  O. Zienkiewicz,et al.  A note on mass lumping and related processes in the finite element method , 1976 .

[24]  Ahmed K. Noor,et al.  Anisotropy and shear deformation in laminated composite plates , 1976 .

[25]  Tarun Kant,et al.  Finite element transient response of composite and sandwich plates with a refined higher-order theory , 1990 .

[26]  E. Hinton,et al.  A note on a thick finite strip method for the free vibration of laminated plates , 1976 .

[27]  Tarun Kant,et al.  A CONSISTENT REFINED THEORY FOR FLEXURE OF A SYMMETRIC LAMINATE , 1987 .

[28]  Ahmed K. Noor,et al.  Finite element analysis of anisotropic plates , 1977 .

[29]  E. Hinton.  A note on a finite element method for the free vibrations of laminated plates , 1976 .

[30]  David R. Owen,et al.  A refined analysis of laminated plates by finite element displacement methods—I. Fundamentals and static analysis , 1987 .

[31]  C. Sun,et al.  Theories for the Dynamic Response of Laminated Plates , 1973 .

[32]  A. K. Noor,et al.  Free vibrations of multilayered composite plates. , 1973 .

[33]  Tarun Kant,et al.  Finite element transient dynamic analysis of isotropic and fibre reinforced composite plates using a higher-order theory , 1988 .