Investigation of the statics and free vibrations of cylindrical shells on the basis of a nonclassical theory

Based on an energy-consistent approach, the equations of motion of an orthotropic shell of arbitrary geometry whose deflected mode is described by equations of the three-dimensional theory of elasticity have been obtained. Three-dimensional equations are reduced to two-dimensional ones by means of the principle of virtual displacements and by the expansion of displacement components into polynomial series in the coordinate system, which is normal to the middle plane of the shell. Modified boundary conditions for standard cases of shell fixturing are formulated. As an example, the paper considers static deformation and natural vibrations of a circular cylindrical shell. Equilibrium equations in displacements and boundary conditions are presented. Calculation of the shell's deflected mode is carried out by means of Laplace transform, thus twofold reducing the number of arbitrary constants in integration of the system of differential equations of the problem. The values of natural frequencies are determined by the Bubnov-Galerkin variational method. The effect of different types of boundary conditions on the deflected mode and the values of natural frequencies is analyzed. The results of calculation of the natural frequencies obtained in this work and those obtained by some versions of the classical Donnell-Mushtari and Goldenweiser- Novozhilov theory, as well as by the three-dimensional theory of elasticity are compared. The results obtained can be used in calculations and strength and durability tests of aviation and space-rocket structures, and also of different-purpose engineering structures. © 2015 by Begell House, Inc.