Dynamic cylindrical shell equations by power series expansions

The dynamics of an infinite circular cylindrical shell is considered. The derivation process is based on power series expansions of the displacement components in the radial direction. By using these expansions in the three-dimensional equations of motions, a set of recursion relations is identified expressing higher displacement coefficients in terms of lower order ones. The new approximate shell equations are hereby obtained from the boundary conditions, resulting in a set of six partial differential equations. These equations are believed to be asymptotically correct and it is, in principle, possible to go to any order. Equations of order up to and including the square of the thickness h2h2 are presented explicitly. This set of six equations are reduced to five as well as three equations and compared to classical theories. Dispersion curves, together with the eigenfrequencies for a 2D case, are calculated using exact, classical and expansion theories. It is shown that the approximate equations containing order h2h2 are in general as good as or better than the established theory of the same order.