“…Then the linear coupling between modes in (3.2) with vanishing right-hand sides can be said to be weak. On discarding μ-terms, (3.5) yield the following separate dispersion relations whenever we implement the inextensibility condition of the middle line of the ring V = 0; see [4]: 8) for bending and azimuthal waves, respectively. In these conditions it is shown that the amplitudes of the azimuthal, A k,n , and bending, B k,n , components of the normal waves are linearly related by B k,n = −ip k,n A k,n (3.9) with coefficients p k,n (k = 1,2), given approximately by The linear dynamical solution (3.8)-(3.10) is usually considered as quite satisfactory.…”