On Vibration of thin Cylindrical Shell immersed in Water and subjected to an Action of Static and Impulsive Pressures

Abstract

A thin elastic shell in form of a circular cylinder is assumed to has small initial deformation. The shell is assumed to suffer the following loads : -(a) At a state of static equilibrium, it is under the action of a normal pressure q1, together with an axial thrust P. (b) During the period o<t<t0, the shell is suddenly acted on by an additional normal pressure q2. (c) At time t0<t onwards, the pressure q2 ceases to act, and the static pressure q1 only acts upon the shell.The Author has made a theoretical study on the vibratory motion of the shell, which is set up by the above loading condition, and has given expressions for deformations of the shell at three periods (a), (b) and (c) as mentioned above.Keeping in mind the case of a pressure-hull of a submarine, which is subjected to an action of impulsive pressure, the effect of virtual mass of surrounding water upon the deformation of shell is also taken into account. The present report (Part I) gives only the theoretical formulae. The discussion about numerical values is expected to appear as Part II of the present Report.