Vibration of Continuous Systems, 2nd Edition

15Vibration of Shells

15.1 INTRODUCTION AND SHELL COORDINATES

A thin shell is a three‐dimensional body that is bounded by two curved surfaces that are separated by a small distance compared to the radii of curvature of the curved surfaces. The middle surface of the shell is defined by the locus of points that lie midway between the two bounding curved surfaces. The thickness of the shell is denoted by the distance between the bounding surfaces measured along the normal to the middle surface. The thickness of the shell is assumed to be constant. Shells and shell structures find application in several areas of aerospace, architectural, civil, marine, and mechanical engineering. Examples of shells include aircraft fuselages, rockets, missiles, ships, submarines, pipes, water tanks, pressure vessels, boilers, fluid storage tanks, gas cylinders, civil engineering structures, nuclear power plants, concrete arch dams, and roofs of large span buildings.

15.1.1 Theory of Surfaces

The deformation of a thin shell can be described completely by the deformation of its middle (neutral) surface. The undeformed middle surface of a thin shell can be described conveniently by the two independent coordinates and shown in Fig. 15.1. In the global Cartesian coordinate system OXYZ, the position ...