Vibration of shallow conical shells with shear flexibility: A first-order theory

A formulation of shear deformation theory implemented numerically for the prediction of vibratory characteristics of shallow conical shell panels is presented. The derivation of thickness shear is assumed in a linear approximation. The Lame parameter for the transverse shear strain component, which has previously been neglected, is considered. This consideration accounts for the replacement of a term in transverse strain distribution through the shell thickness which results in linear transverse shear strain distribution in contrast to the constant distribution hitherto known to researchers in this field. The energy integral, which incorporates the shear deformation and rotary inertia, is minimized to derive the governing eigen-matrix equation. A set of benchmark frequency solutions is presented for two exemplary conical shells: the cantilever and the fully clamped shells. Some selected mode shapes in terms of mid-surface contour plots and three-dimensional meshes are also illustrated.