A higher-order theory for vibration of doubly curved shallow shells

A higher-order shear deformation theory is presented for vibration analysis of thick, doubly curved shallow shells. An orthogonal curvilinear coordinate system is employed to arrive at the strain components. A third-order displacement field in transverse coordinate is adopted. Though no transverse normal stress is assumed, the theory accounts for cubic distribution of the transverse shear strains through the shell thickness in contrast with existing parabolic shear distribution. The unsymmetric shear distribution is a physical consequence of the presence of shell curvatures where the stress and strain of a point above the mid-surface are different from its counterpart below the mid-surface. Imposing the vanishing of transverse shear strains on top and bottom surfaces, the rotation field is reduced from a six-degree to a two-degree system. The discrepancy between the existing and the present theories is highlighted.