Natural frequencies and stability for Z-shaped fluid-conveying pipes with constrained-layer damping – Semi-analytic modeling with experimental validation

As the common fluid-conveying component, pipe structures are susceptible to excessive vibration due to internal fluid and external excitation. Constrained-layer damping (CLD) is commonly applied to suppress structural vibrations. However, effective modeling and vibration suppression analysis for Z-shaped fluid-conveying pipes are lacking to explore novel dynamic behaviors. This paper presents a dynamic model for analyzing the three-dimensional vibration of Z-shaped fluid-conveying pipes treated by partial CLD based on the semi-analytical method. Utilizing Timoshenko beam theory and calculating the centrifugal, Coriolis, and inertial force of fluids, the energy of straight and curved fluid-conveying pipes treated by CLD is derived. Based on the Lagrangian energy function, the equation of motion is obtained by using the Rayleigh-Ritz method. The improved artificial spring set is deployed to model the interaction of pipe sections and the non-uniform constraint distribution of clamps. Modal parameters are obtained by solving characteristic equations. The proposed method is verified by comparisons with references and modal experiment results. Frequency parameters, damping effects, and stability are analyzed under various fluid, geometric, and CLD parameters. In conclusion, a novel dynamic model is provided for analyzing the vibration and stability of the Z-shaped fluid-conveying pipe treated by CLD, which lays a foundation for vibration suppression research of fluid-conveying pipe systems.