VIBRATION OF THICK DOUBLY-CURVED STRESS-FREE SHALLOW SHELLS OF CURVILINEAR PLANFORM

This paper presents the formulation and numerical analysis for free vi bration of a class of thick, shear deformable stress free shallow shel ls. Using the Ritz energy approach, the higher-order shell theory is p resented with a set of globally versatile shape functions. The eigenva lue equation is formulated and solved to obtain the natural frequencie s and mode shapes of the thick shells of elliptic planform. As expecte d, a comparison between thin and thick shell results shows the thin sh ell theory that ignores transverse shear deformation, and rotary inert ia overestimates the flexural stiffness and thus the vibration frequen cy. The curvature and shallowness ratios have minor effects on the vib ratory characteristics of thick shells. A set of first known contour a nd three-dimensional displacement mode shapes is also presented to ill ustrate the vibration nature of thick shells.