Axially Symmetric Motions of Thick Cylindrical Shells

An approximate theory of axially symmetric motions of thick, elastic, cylindrical shells, in which the effect of transverse normal stress is retained, is deduced from the three-dimensional theory of elasticity. The present theory contains, in addition to the usual membrane and bending terms, also the influence of rotatory inertia and transverse shear deformation. Thus it may be specialized to a variety of shell, plate, and solid-cylinder equations. The propagation of free harmonic waves in an infinite shell is studied on the basis of the present theory and the three-dimensional theory of elasticity. Excellent agreement is obtained for the phase velocity of the lowest mode of motion for a wide range of the parameters involved.