Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory

This paper deals with the free vibration of open, laminated composite, circular cylindrical panels having a rectangular plan-form and all their edges free of external tractions. The material arrangement of the shell panels considered may vary from this of the single isotropic (or special orthotropic) layer to that of a general angle-ply lay-up. The analysis is based on the application of the Ritz approach on the energy functional of the Love-type version of a unified shear deformable shell theory. A through-thickness parabolic distribution of the transverse shear deformation is mainly assumed but, for comparison purposes, numerical results that are based on the assumptions of the classical Love-type shell theory are also presented. The Ritz method is a powerful analytical technique since, provided that a complete set of trial functions is employed, it can provide the exact solution of the problem considered in infinite series forms. The mathematical formulation is therefore presented in a general form, appropriate for any set of basis functions. The variational approach is, however, finally applied in conjunction with a complete functional basis made of the appropriate admissible orthonormal polynomials. (C) 1999 Elsevier Science Ltd. All right reserved.