Second-order nonlinear dynamics of catenary pipelines subjected to bi-chromatic excitations

Abstract

Please cite this article as: I.K. Chatjigeorgiou, Second-order nonlinear dynamics of catenary pipelines subjected to bi-chromatic excitations, Appl. Math. Modelling (2014), doi: http://dx. AbstractThe purpose of this study is to investigate the 2D nonlinear dynamics of catenary pipelines for marine applications approaching the solution in the frequency domain. The proposed methodology is seeking the transfer functions and in particular the quadratic magnification factors of the involved dynamic components assuming a bi-chromatic excitation, namely, a signal which arises from the superposition of two different sinusoidal harmonics. The sought solution is achieved by employing a perturbation technique that expands all dynamic components into series of perturbations relatively to a scaling factor, whilst the mathematical processing is performed into the complex space. The adopted procedure results in a series of problems which are solved separately and successively.Also, separate mathematical systems are derived for the sum-and the difference-frequency problems. The numerical results are obtained using a centered-differences approximation of the final set of ordinary differential equations. The correlation of the structural model with marine applications required the employment of a proper procedure for linearizing the nonlinear drag force at second-order. Finally, it is remarked that the outlined methodology can be effectively extended to polychromatic excitations and to the 3D space as well.