Nonlinear resonances of parametrically excited risers-numerical and analytic investigation for Ω = 2ω1

The paper deals with the internal resonances originated from parametric excitation of a slender pipe conveying fluid for marine applications. The reported work focuses on a specific case study, which corresponds to an excitation frequency that is equal to the double of the structure's first lateral natural frequency. The features of the numerical predictions are enlightened through the analytic treatment of the problem, which is carried out using the method of multiple scales. The describing model takes into account both linear and quadratic damping components. For enabling the analytic approximation, only the first two time-dependent modes of the lateral motion are retained. After extensive mathematical manipulations and appropriate simplifications closed-form solutions have been obtained. Finally, the conclusions drawn through the numerical solution of the problem are compared and validated against analytical results.