A HIGHER-ORDER THEORY FOR VIBRATION OF SHEAR-DEFORMABLE CYLINDRICAL SHALLOW SHELLS

The vibratory characteristics of thick cylindrical shallow shells of r ectangular planform is investigated in this paper, A higher order shea r deformation theory is proposed to analyse the effects of various she ll geometries and boundary conditions on the vibration responses. The present higher order theory results in cubic expressions for the trans verse shear distribution through shell thickness. The strain and kinet ic integral energy expressions involving higher order shear deformatio n are derived in terms of Cartesian coordinates. An energy functional based on the principle of extremum energy is employed which yields a g overning eigen-matrix equation. A set of orthogonally generated two-di mensional polynomial functions is adopted to approximate the deflectio ns and rotations of the shells. The results, where possible, are compa red with the available experimental and existing numerical results. Se ts of new results for the hard simply supported and fully clamped cyli ndrical shallow shells are presented. Selected modes are illustrated i n three-dimensional displacement plots.