Analysis of damped composite sandwich plates using plate bending elements with substitute shear strain fields based on Reddy's higher-order theory

Abstract Two new C 0 assumed strain finite element formulations of Reddy's higher-order theory are used to determine the natural frequencies and loss factors of layered anisotropic composite and sandwich plates. Material properties typical of fibre polyester resins for the skin and HEREX C70 PVC foam damping materials for cores are used to show the parametric effects of plate aspect ratio, length-thickness ratio on natural frequencies and loss factors. A consistent mass matrix is adopted in the present formulation. Both frequency-independent and frequency-dependent damping of viscoelastic materials are considered. The developed elements are free from spurious zero energy modes due to the assumed strain approach.

[1]  Zvi Hashin,et al.  Complex moduli of viscoelastic composites—II. Fiber reinforced materials , 1970 .

[2]  Andrew S. Bicos,et al.  Analysis of free damped vibration of laminated composite plates and shells , 1989 .

[3]  Richard H. Macneal,et al.  A simple quadrilateral shell element , 1978 .

[4]  K. Rohwer,et al.  Application of higher order theories to the bending analysis of layered composite plates , 1992 .

[5]  P. Cupiał,et al.  Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer , 1995 .

[6]  G. Lesieutre,et al.  Fiber Contribution to Modal Damping of Polymer Matrix Composite Panels , 1995 .

[7]  F. Ju,et al.  Finite Element Analysis on Modal Parameters of Anisotropic Laminated Plates , 1988 .

[8]  J. N. Reddy,et al.  A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates , 1986 .

[9]  J. N. Reddy,et al.  Analysis of laminated composite plates using a higher‐order shear deformation theory , 1985 .

[10]  Stefanos Vlachoutsis,et al.  Shear correction factors for plates and shells , 1992 .

[11]  R. Adams,et al.  The dynamic properties of carbon-glass fibre sandwich-laminated composites: theoretical, experimental and economic considerations , 1984 .

[12]  J. C. Simo,et al.  On the Variational Foundations of Assumed Strain Methods , 1986 .

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

[14]  T. Hughes,et al.  Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element , 1981 .

[15]  Robert D. Adams,et al.  Effect of Fibre Orientation and Laminate Geometry on the Dynamic Properties of CFRP , 1973 .

[16]  E. Hinton,et al.  A nine node Lagrangian Mindlin plate element with enhanced shear interpolation , 1984 .

[17]  E. Hinton,et al.  The finite element analysis of homogeneous and laminated composite plates using a simple higher order theory , 1986 .

[18]  J. N. Reddy,et al.  A refined nonlinear theory of plates with transverse shear deformation , 1984 .

[19]  Ahmed K. Noor,et al.  Computational Models for Sandwich Panels and Shells , 1996 .

[20]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

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

[22]  R. A. Shenoi,et al.  Dynamic analysis of composite sandwich plates with damping modelled using high-order shear deformation theory , 2001 .

[23]  Kshitij Gupta,et al.  Damping studies in fiber-reinforced composites : a review , 1999 .

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

[25]  J. N. Reddy,et al.  ANALYSIS OF COMPOSITE PLATES USING VARIOUS PLATE THEORIES, PART 2: FINITE ELEMENT MODEL AND NUMERICAL RESULTS , 1998 .

[26]  J. N. Reddy,et al.  Analysis of composite plates using various plate theories -Part 1: Formulation and analytical solutions , 1998 .

[27]  Medhat A. Haroun,et al.  Reduced and selective integration techniques in the finite element analysis of plates , 1978 .

[28]  J. N. Reddy,et al.  A penalty plate‐bending element for the analysis of laminated anisotropic composite plates , 1980 .

[29]  J. N. Reddy,et al.  An assessment of four‐noded plate finite elements based on a generalized third‐order theory , 1992 .

[30]  R. Shenoi,et al.  Free vibration analysis of composite sandwich plates , 1999 .

[31]  E. Hinton,et al.  A family of quadrilateral Mindlin plate elements with substitute shear strain fields , 1986 .

[32]  Rakesh K. Kapania,et al.  A survey of recent shell finite elements , 2000 .

[33]  A. Bhimaraddi.  Sandwich beam theory and the analysis of constrained layer damping , 1995 .

[34]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[35]  R. Adams,et al.  Prediction and Measurement of the Vibrational Damping Parameters of Carbon and Glass Fibre-Reinforced Plastics Plates , 1984 .

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