On the Role of Bending in the Dynamic Response of Thin Shells to Moving Discontinuous Loads

Abstract

An infinite cylindrical shell symmetrically loaded by a step pressure wave is used to study the importance of bending in a dynamic system with a moving, discontinuous load. The case of an acoustically loaded thin steel shell in water is discussed at length. A parameter study is run to determine the effect on shell behavior of changes in load speed, external damping, and shell thickness. I t is found that bending plays quite different roles in static (or quasi-static) and dynamic systems. In a static system, discontinuities in displacements and stresses appear at points of load discontinuity unless bending is taken into account. Also, the bending stresses themselves are significant in the neighborhood of such points. Similar results hold when a quasi-static system is considered—i.e., when the inertial reaction of the shell is neglected but the load is allowed to move. In the dynamic system, however, membrane theory alone is sufficient to yield a continuous solution. The importance of bending in such a system is closely linked to the speed of the load and the thickness of the shell. I t is shown that, contrary to the impression gained from a static analysis, it is often possible to neglect bending provided the load speed is fairly large (three or four times the acoustic speed of air), and the shell is sufficiently thin (thickness-radius ratio < l / 3 0 ) . V =