Vortex Induced Vibration of Simply Supported Visco elastic Beam

In this paper, vortex induced vibration of simply supported viscoelastic beam were investigated using semi-analytical method. By applying the general form of the viscoelastic model, the nonlinear partial differential equations of motion based on the Euler Bernoulli beam’s theory and displacement coupling fluid-structure interaction model were obtained via the Newton’s second law. A classical nonlinear van der Pol equation was taken as the governing equation for one component of the vortex shedding force on the beam. Employing the Galerkin discretization method, the equations of motion are reduced to a set of nonlinear ordinary differential equations with coupled terms and then there have been solved numerically by Runge-Kutta method. Finally, the effect of system parameters on the time response, phase plane and maximum amplitude of the beam are investigated. The results indicate that the viscoelastic behavior have a significant influence on the dynamic characteristics of the system and causes to change the Lock-in phenomenon with respect to corresponding elastic system. For example, for E2=10E1 the viscoelastic behavior can change the position of the locking area, and the maximum amplitude of the beam is increased by 45%. Lock-in from of vortex-induced vibrations was considered as a possible source of increased fatigue and damage. Therefore, by using viscoelastic materials the maximum amplitude of the system is reduced and the Lock-in condition can be changed. Additionally, based on the significant influence of viscoelastic behavior on the dynamic characteristics of the system, viscoelastic behavior should be considered in the mathematical model of the systems.