Recently, Raju and Rao , published a finite element solution to the large amplitude vibrations of thin shells of revolution, obtaining a frequency amplitude relationship of a hardening nature for a circular cylindrical shell. This prompted Evensen to point out that the large amplitude vibrations of a cylindrical shell is of a softening nature. He cites his theoretical formulation [3] and several other papers, including experimental evidence . This letter, surprisingly, excludes any reference to two important contributions: the derivation of the modal equations to the title problem by Dowell and Ventres [5] and a solution to these modal equations by Atluri [6]. Reference [6] in fact indicates that the non-linear vibrations of a circular cylindrical shell are of the hardening type.
The crux of the problem, the present author believes, lies in the understanding of the physics of the problem. This is outlined below.
The differential equations [5], consist of an equation of equilibrium containing the transverse displacement w and the stress function F, and another equation of compatibility relating Fto a linear and quadratic terms in w. The compatibility equation can be solved for a given mode shape (more about choice of mode shape later) to give F~, the particular integral, and Fc, the complementary solution to the homogeneous part of the equation. Evensen in his solution does not consider the complementary solution at all but instead, tries to satisfy