Abstract
The vibratory characteristics of thick cylindrical shallow shells of rȩctangular planform is investigated in this paper. A higher order shear deformation theory is proposed to analyse the effects of various shell geometries and boundary conditions on the vibration responses. The present higher order theory results in cubic expressions for the transverse shear distribution through shell thickness. The strain and kinetic integral energy expressions involving higher order shear deformation are derived in terms of Cartesian coordinates. An energy functional based on the principle of extremum energy is employed which yields a governing eigen-matrix equation. A set of orthogonally generated two-dimensional polynomial functions is adopted to approximate the deflections and rotations of the shells. The results, where possible, are compared with the available experimental and existing numerical results. Sets of new results for the hard simply supported and fully clamped cylindrical shallow shells are presented. Selected modes are illustrated in three-dimensional displacement plots.
Published Version
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