Investigation on internal resonance of fluid conveying pipes with initial geometric imperfection

Abstract

This paper shows numerical research on the 1:2 internal resonance and chaotic bifurcation phenomena of the graphene platelets reinforced metal foams (GPLRMF) pipes, with emphasis on the effect of initial geometric imperfection. To this end, combining the high order shear deformation beam theory and Kelvin-Voigt viscoelasticity, a mathematical model that considers geometric imperfection is established. The fluid in pipeline is supposed to be incompressible and inviscid. Subsequently, the Galerkin discretization and multiscale method are utilized for solving the nonlinear governing equations in the case of 1:2 internal resonance. And the nonlinear dynamic behavior of the fluid conveying pipes can be analyzed through the frequency amplitude diagrams, bifurcation curves, time course curves, phase trajectories, and Poincaré maps. The double jump phenomena are excited to demonstrate the dynamic characteristics of the pipes with 1:2 internal resonance. In the case of small disturbance coefficients, various internal resonance and chaos phenomena can be captured in the pipeline system. Research shows that the coupled effects between initial geometric imperfection and nonlinear geometric relationships is non-monotonic. That is to say, for bimodal internal resonance, when the initial geometric imperfection increase, the unstable region will be compressed, and the response amplitude will increase.