Nonlinear vibration analysis of a fluid-conveying pipe under harmonic excitation with elastic boundary constraints

Abstract

Fluid-conveying pipes are extensively used in practical engineering in various industries and play an important role in industry and daily life. Under complicated working conditions, inevitable vibrations affect the stability and integrity of these pipes, drawing significant academic attention. Typically, the dynamic modeling of these pipes considers ideal rigid boundary conditions, including fixed support, simply support, and cantilever pipes, ignoring the effects of boundary elasticity. This paper investigates the effects of boundary elasticity on the harmonic excitation responses in sub-critical and super-critical regimes. The governing equations and boundary conditions are derived via the extended Hamilton's principle. Later, the non-trivial equilibrium configuration is analytically deduced, and the governing equations for fluid-conveying pipes with elastic supports are discretized into a set of nonlinear ordinary differential equations using the Galerkin method. The harmonic balance method (HBM) is employed to solve these differential equations, with its accuracy validated against the Runge-Kutta method. Finally, numerical examples are conducted in sub-critical and super-critical regimes to show the effects of boundary vertical stiffness, torsional stiffness, fluid velocity, and excitation on solution stability, natural frequencies, and amplitude of the steady-state response at the middle point. This paper provides important guidance for the design of boundary elasticity in sub-critical and sup-critical fluid-conveying pipes.