The Influence of Boundary Constraint Viscoelasticity on the Nonlinear Forced Vibration of Fluid-Conveying Layered Pipes †

In this paper, the influence of the viscoelasticity of boundary constraints on the forced vibration of the nonlinear forced resonance of a fluid-conveying layered pipe under an external forced excitation is studied. The pipe lays on viscoelastic foundations and is simply supported at both ends, and one end is subject to a viscoelastic boundary constraint. The Kelvin–Voight model was employed to describe the viscoelasticity provided by the foundation and boundary constraint. Hamilton’s variational principle was used to obtain the governing equations, during which geometric nonlinear factors including curvature nonlinearity and inertia nonlinearity were considered. By employing a perturbation-incremental harmonic balance method (IHBM), amplitude–frequency bifurcation diagrams of the pipe were obtained. The results show that the viscoelastic constraints from the boundary and foundation have significant influence on the linear and nonlinear dynamic behavior of the pipe system.