Bifurcation Analysis and Parameter Influences in Pipes Conveying Fluid with Nonlinear Energy Sink

This paper investigates parameter influence and bifurcation of harmonically excited fluid-conveying pipes with a nonlinear energy sink (NES) via the incremental harmonic balance (IHB) method. Compared to previous numerical calculations, the IHB method adopted here facilitates analysis of parameter influence and bifurcation. First, a mathematical model in the form of a high-order partial differential equation is deduced for the fluid-conveying pipe under harmonic loading using Hamilton’s principle. This model is then transformed into a nonlinear ordinary differential equation through Galerkin truncation. Second, algebraic equations are derived using the IHB method, and the amplitude–frequency curves of the system are obtained by employing the frequency, amplitude, and arc-length increment techniques. Third, the stability and bifurcation of the system’s periodic solutions are investigated using Floquet theory in conjunction with Hsu’s method. Finally, the energy absorption performance of the NES system under varying parameters is investigated. The solutions obtained through the IHB method are found to be in good agreement with those obtained using the Runge–Kutta method. Furthermore, numerical examples are provided to comprehensively analyze the parameter influence and bifurcation characteristics of the system.