Asymptotic integration of the 2D equations of motion for an inhomogeneous thin elastic shell

In this study, low-frequency dispersion analysis of cylindrical thin shells is carried out by asymptotic approximation using special scalings and compared with the theories in the literature. In particular, this asymptotic approach is applied to 3D general elasticity equations and 1D equations are obtained at the mid-surface for the problems considered in the thesis. For each problem, new results are obtained that are consistent with and contribute to the literature.\par In the analysis of the first problem, the 2D annulus, it is shown that the even part of the circumferential stress is not constant with respect to the thickness and is polynomial in form, which is contrary to the characteristic of the mechanical behavior related to the almost inextensible mid-plane effect. As a second problem, an approximate 1D fourth-order equation for a 3D thin shell cylinder is obtained based on the assumption that the ratio of the shell thickness to the radius is of the same order as the ratio of the radius to a typical wavelength, and it is found that most of the coefficients in the equation coincide with their counterparts in Sanders-Koiter shell theory. Finally, the low-frequency vibrations of a thin-shell functionally graded (FGM) cylinder are considered in the plane strain framework. Similarly, a consistent approximate equation of motion at the mid-surface is derived using special scaling and dynamic relations in elasticity. The original formulas for the variation of natural frequencies and all stress components arising from the derived equation are obtained.