Dynamics of a harmonically excited nonlinear pipe conveying fluid equipped with a local nonlinear energy sink

Abstract

When the magnitude of the lateral elastic deformation of a pipe over its length is more prominent than in a linear situation, it is necessary to use nonlinear terms to reduce the gap between the mathematical model and the real system. Also, the importance of nonlinear terms is more considerable when a pipe conveying fluid is studied. Since the passive vibration control of pipes is of great significance, one may employ a nonlinear energy sink (NES) as the control configuration attached to the pipe. Hence, in this study, the dynamics of a harmonically excited nonlinear pipe conveying fluid attached to a local NES is investigated. The boundary conditions are assumed doubly clamped. The two nonlinear partial differential equations of motion are derived. Using the method of Galerkin, considering four shape modes, five nonlinear coupled equations are obtained for describing the pipe and NES’s models. The most applicable outcome of this research is preventing the chaotic motion, when the pipe is equipped by the NES at one-fourth of one of its ends. Chaotic regions might take whole different forms for a linear pipe conveying fluid.