TABLE OF CONTENTS A thin circular cylindrical shell made of isotropic, homogeneous and linearly elastic material is considered, so that classic theories of shells are applicable. Many linear theories of shells have been developed. In this section, only the Donnell and Fl gge-Lur e-Byrne theories of shells are considered; these are obtained by neglecting nonlinear terms in the Donnell and Fl gge-Lur e-Byrne nonlinear shell theories. In particular, the Fl gge-Lur e-Byrne theory gives very accurate results for isotropic thin shells.
The shell is constrained at both ends by very thin diaphragms resistant to shear forces, but, at the same time, extremely flexible to loads orthogonal to their plane. This constraint is called simply support or shear diaphragm. The boundary conditions, referring to Figure 1.12, are given as
where u, ?, w are the displacements of a generic point in the longitudinal, circumferential and radial direction, respectively; N x is the normal force, M x is the bending moment per unit length, and L is the shell length.
The equations of motion for linear vibrations of circular cylindrical shells are obtained from the nonlinear ones canceling nonlinear terms. For Donnell s theory of shells, equations (1.52 1.54) represent the nonlinear equations of motion. The equation of motion in the radial direction is given by substituting equation (1.142a c) into (1.52) and canceling all the nonlinear terms. The in-plane equations are obtained by substituting f x = ?h and f ? =
