A second-order approximation of multi-modal interactions in externally excited circular cylindrical shells (Q5959338)

The authors consider the nonlinear behaviour of infinitely long circular cylindrical shell subject to harmonic radial load whose frequency is approximately equal to the natural frequency of two orthogonal flexural modes, which is equal to one-half the natural frequency of breathing mode. The limit cycle solution, two-to-one resonance, one-to-one resonance, bifurcation and chaos are investigated. Reviewer's remark: Unfortunately, the description is non-concrete and does not allow a detailed analysis of the obtained results. Probably, the formulas and equations are derived by means of a computer in symbolic form, and thus it is very difficult to prove them.