Abstract
Equations of motion of shells are formulated in curvilinear co-ordinates that are consistent with assumptions made in the Timoshenko beam and also the Mindlin plate equations. This consistency is proven by obtaining the Timoshenko and Mindlin equations from the derived shell equations by geometrical reduction. The implication of the Timoshenko type shear is illustrated by constrasting the free vibration behavior of the special case of a cylindrical shell with the behavior of the Timoshenko beam and the Mindlin plate.
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