Irreversible passive energy transfer of an immersed beam subjected to a sinusoidal flow via local nonlinear attachment

Abstract

Passive vibration control of immersed structures in deep water subjected to the external fluid flow has rarely been studied. With the aim of passively absorbing, vibration of a doubly fixed beam under a sinusoidal flow using a nonlinear attachment is studied in this paper. The beam is modeled using the Euler-Bernoulli beam theory. The essentially nonlinear attachment has purely cubic stiffness and linear damping. Required conditions for occurring relaxation oscillations, Hopf and saddle-node bifurcations in the system response are studied. Analytical and numerical approaches are used to analyze the steady-state responses of the considered model. In addition, the influence of the location, the damping and the stiffness of the nonlinear absorber and external load are investigated on the dynamical behavior of the system. Furthermore, influence of the attachment stiffness on quasi-periodic motion boundaries surveyed. It is shown that in the presence of the nonlinear energy pumping the amplitude of the system response decreases significantly and as the attachment location approaches the beam supports the occurrence of the relaxation oscillations decreases and saddle-node bifurcations take place in the system response. The presented results and the proposed modeling approach can be used to design and enhance the performance of nonlinear vibration absorbers for subsea structures.