A HIGHER-ORDER THEORY FOR VIBRATION OF DOUBLY-CURVED SHALLOW SHELLS

A higher-order shear deformation theory is presented for vibration ana lysis of thick, doubly curved shallow shells. An orthogonal curvilinea r coordinate system is employed to arrive at the strain components. A third-order displacement field in transverse coordinate is adopted. Th ough no transverse normal stress is assumed, the theory accounts for c ubic distribution of the transverse shear strains through the shell th ickness in contrast with existing parabolic shear distribution. The un symmetric 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 s urfaces, the rotation field is reduced from a six-degree to a two-degr ee system. The discrepancy between the existing and the present theori es is highlighted.