Vibration of thick doubly-curved stress free shallow shells of curvilinear planform

This paper presents the formulation and numerical analysis for free vibration of a class of thick, shear deformable stress free shallow shells. Using the Ritz energy approach, the higher-order shell theory is presented with a set of globally versatile shape functions. The eigenvalue equation is formulated and solved to obtain the natural frequencies and mode shapes of the thick shells of elliptic planform. As expected, a comparison between thin and thick shell results shows the thin shell theory that ignores transverse shear deformation, and rotary inertia overestimates the flexural stiffness and thus the vibration frequency. The curvature and shallowness ratios have minor effects on the vibratory characteristics of thick shells. A set of first known contour and three-dimensional displacement mode shapes is also presented to illustrate the vibration nature of thick shells.