Vibration suppression of pipe conveying fluid using a nonlinear absorber in longitudinal direction

Abstract

The article outlines the design of a nonlinear absorber that features cubic stiffness. The absorber was created for a pipe conveying fluid and was based on the internal resonance mechanism. To create the nonlinear absorber, a sliding mass oscillator was attached along to the pipe conveying fluid. Nonlinear equations were derived using Hamilton's principle. The flowing fluid was considered both as a constant value and a fluctuating term. To investigate the nonlinear behavior of the coupled pipe-absorber system, the direct multiple scales method was used. By selecting appropriate values of mass and stiffness for the absorber, the natural frequency of the absorber was tuned in three cases: 1–1, 2–1, and 3–1 internal resonance ratios between the natural frequency of the absorber and the first natural frequency of the pipe. The goal of the mechanism was to transfer energy from the pipe to the absorber, and the design was successful in achieving this. A saturation phenomenon was detected in the force modulation response at the three-to-one internal resonance. The results showed a reduction in amplitudes in both frequency and force response curves under the external primary resonance and pulsating flowing fluid in the supercritical regime. The nonlinear absorber has a good performance in a wide range of flow velocity and excitation. The accuracy of the results was verified using Galerkin and Finite difference methods.