Vibration control of FG-pipe conveying fluid using a nonlinear absorber with nonlinear damping in longitudinal direction

Abstract

This study investigates the use of a nonlinear absorber with nonlinear damping to mitigate the transverse vibrations of a fluid-conveying pipe made of functionally graded materials (FGM). The nonlinear effects arising from the pipe’s curvature and inertia are precisely accounted for in the equation of motion. The governing equations of the FGM pipe-nonlinear absorber system are derived using extended Hamilton’s principle and solved using the method of multiple scales. 1:1 internal resonance condition between the first natural frequency of the pipe and absorber is explored for transferring energy from the pipe to the absorber based on the modal interaction. The frequency-amplitude curves reveal that as the power-law index (n) increases, the nonlinear hardening behavior of the pipe decreases, while that of the absorber increases. Incorporating nonlinear damping in the absorber is found to further improve vibration suppression, leading to a strongly modulated response that reduces the pipe vibrations by over 84.57% and the absorber vibrations by over 94.57%. The impact of the absorber’s nonlinear stiffness on the strongly modulated response is also investigated, indicating that excessively high stiffness can cause the disappearance of this beneficial behavior. The findings of this study provide valuable insights into the optimal design of FGM pipes conveying fluid and the integration of nonlinear absorbers with nonlinear damping for enhanced vibration mitigation.