Vibration control in fluid conveying pipes using NES with nonlinear damping

Control of vibrations in fluid transmitting pipes has emerged as a major engineering challenge. For higher fluid flow rate, support vibration, and excitation load, the vibrations in pipes that convey fluid can be complex and, at times, catastrophic. Recent works have demonstrated that Nonlinear Energy Sink (NES) can be effectively employed for passive vibration control of fluid-conveying pipes. The present work explores the possibility of using NES with nonlinear damping to overcome the limitations of conventional NES-based vibration control in fluid-transmitting pipes. Geometric nonlinear damping (velocity-displacement dependent damping), whose physical realization is possible by a suitable geometric configuration of the linear viscous damper, is considered in this study. Euler–Bernoulli beam theory models the fluid conveying pipe under an external harmonic load. The reduced order model obtained through the Galerkin procedure is investigated analytically using the complex averaging method. The occurrence of strongly modulated and weakly modulated responses are demonstrated, and their effect on vibration mitigation is shown. The frequency range exhibiting strongly modulated response in the system is significantly increased with the addition of nonlinear damping to NES. This assists in mitigating pipe vibrations by initiating targeted energy transfer from pipe to NES. The Saddle–Node and Hopf bifurcation boundaries in the model are identified using the slow-flow dynamics obtained by complex averaging. The effect of nonlinear damping, external excitation, the location of NES, and the flow rate on the bifurcation boundaries are investigated in detail. It is shown that the external excitation needed to trigger Saddle–Node bifurcation is largely reduced for NES having nonlinear damping. Furthermore, a study of Hopf bifurcation in the frequency domain shows that using NES with nonlinear damping significantly decreases the frequency range in which high-amplitude isolated solutions occur. The method of multiple scales is used to derive the analytical expression for the slow invariant manifold of the pipe-NES system. The vibration suppression mechanism and the occurrence of strongly modulated responses are explained with the help of flow on slow invariant manifolds. A comparison of the topology of the slow invariant manifolds shows that using nonlinear damping with NES substantially reduces the vibration amplitude of the pipe structure. The percentage of energy transferred to the NES is quantified to show the effectiveness of the proposed absorber over normal NES for different flow speeds.