Further comments on nonlinear vibrations of shells

THE RECENT LETTER by Dowell (1998) touched on several aspects of the literature and thephysics of nonlinear vibrations of circular cylindrical shells, clarifying some of the issueswhile attempting to reconcile some hitherto contradictory Þndings, and at the same timeoutlining some of the unresolved issues and potentially proÞtable directions for furtherresearch.The letter provided us with the impetus for some further thoughts on the subject, and herewe o¤er some complementary discussion to a few of the points raised by Dowell (1998) andclariÞcations to our own work (Amabili et al. 1998).The Þrst issue is that of the magnitude of the nonlinear e¤ects associated with forcedmotions of a simply supported, circular cylindrical shell. As pointed out by Dowell (1998),the degree of nonlinearity can be extremely weak: of the order of 0.5% (vis-a`-vis the linearfrequency) for amplitudes of the driven mode equal to the shell thickness. Such a small e¤ectrenders deliberation on whether the e¤ect is hardening or softening almost immaterial.......