On mathematical modeling, analysis and vibration control of a submarine pipeline conveying fluid and subjected to a regular wave excitation

We consider the problem of nonlinear vibration response analysis and control of a submarine pipeline model conveying fluid and subjected to regular wave excitation. Wave excitation is modeled as a hydrodynamic force consisting of inertial and Morison-type drag components. After a brief description of the physical model, the governing equations of the system, with and without control, are established using the generalized Hamiltonian variational principle. A nonlinear energy sink (NES)-type controller is employed to reduce the vibration amplitude of the pipeline model. An analytical technique based on the multiple time scale method is applied to the linearized system to illustrate how parameters such as the internal fluid flow velocity, controller parameters, and wave amplitude affect the system’s response. The results indicate that as the internal fluid flow velocity increases, the resonant amplitude of the pipeline vibration also increases. This means that a high value of this velocity can contribute to destabilizing the system. Similarly, increasing the wave excitation intensity leads to an increase in the resonance (peak amplitude) of the pipeline. This important finding demonstrates that the highest wave excitation intensity can cause large displacements and contribute to destabilizing the structure. To highlight what we consider an original contribution, the fluctuations generated by the approximation of the drag force after approximation show a notable increase in the peak resonance amplitude of the structure. This load parameter can cause large displacements of the pipeline, potentially leading to significant consequences for the structure. Overall, the study demonstrates that the NES-type controller provides a considerable vibration attenuation rate, which is beneficial for system safety. Numerical simulations applied to the reduced nonlinear governing equations of the system are carried out to confirm the analytical predictions.