Free vibration of shear-flexible anti-symmetric angle-ply doubly curved panels

Abstract A hitherto unavailable analytical solution to the boundary-value problem of free vibration of an anti-symmetric angle-ply laminated shear-flexible doubly curved shell of rectangular planform is presented. A novel solution methodology, based on a boundary-continuous double Fourier series approach, is developed to solve the eigenvalue problems, involving five highly coupled linear partial differential equations with constant coefficients, resulting from Sanders' FSDT (first-order shear-deformation theory)-based formulation that also includes surface-parallel and rotatory inertias. Numerical results presented in this study exhibit, for the first time, a mode switch of numerically ordered frequencies from transverse to surface-parallel modes with the change of such geometric and material parameters as length-to-thickness ratio, radius-to-thickness ratio and lamination angle. Additionally, these results have been utilized to validate the accuracy of available CLT-bascd approximate solutions, computed using the Galerkin approach.

[1]  K. Soldatos.  FREE VIBRATIONS OF ANTISYMMETRIC ANGLE-PLY LAMINATED CIRCULAR CYLINDRICAL PANELS , 1983 .

[2]  Raphael Loewy,et al.  On vibrations of heterogeneous orthotropic cylindrical shells. , 1971 .

[3]  S. T. Gulati,et al.  Effects of Anisotropy in Axisymmetric Cylindrical Shells , 1967 .

[4]  L. S. D. Morley,et al.  AN IMPROVEMENT ON DONNELL'S APPROXIMATION FOR THIN-WALLED CIRCULAR CYLINDERS , 1959 .

[5]  Nicholas J. Hoff,et al.  Buckling of Axially Compressed Circular Cylindrical Shells at Stresses Smaller Than the Classical Critical Value , 1965 .

[6]  C. Chia.  Nonlinear analysis of plates , 1980 .

[7]  Jack R. Vinson,et al.  Laminated Transversely Isotropic Cylindrical Shells , 1971 .

[8]  P. K. Sinha,et al.  Transverse Bending of Cross-Ply Laminated Circular Cylindrical Plates , 1976 .

[9]  J. N. Reddy,et al.  Exact Solutions of Moderately Thick Laminated Shells , 1984 .

[10]  Stanley B. Dong,et al.  On the Theory of Laminated Anisotropic Shells and Plates , 1962 .

[11]  A. Green,et al.  LXXXII. The buckling of flat rectangular plywood plates , 1945 .

[12]  Charles W. Bert,et al.  Vibration of cylindrical shells of bimodulus composite materials , 1981 .

[13]  H. S. Morgan,et al.  Buckling and Vibration of Cross-Ply Laminated Circular Cylindrical Shells , 1974 .

[14]  Stanley B. Dong,et al.  On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation , 1972 .

[15]  J. B. Greenberg,et al.  Buckling and vibration of orthotropic composite cylindrical shells , 1980 .

[16]  K. Soldatos,et al.  Buckling and vibration of cross-ply laminated circular cylindrical panels , 1982 .

[17]  J. N. Reddy,et al.  THERMOELASTICITY OF CIRCULAR CYLINDRICAL SHELLS LAMINATED OF BIMODULUS COMPOSITE MATERIALS , 1981 .

[18]  Kamal R. Abu-Arja,et al.  Static analysis of moderately-thick finite antisymmetric angle-ply cylindrical panels and shells , 1991 .

[19]  H. Kabir,et al.  A generalized Navier's approach for solution of clamped moderately-thick cross-ply plates , 1991 .