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The violent vibration of truss structures may cause fatigue, faults, or even an accident. Aiming to analyze the vibration power flow and transfer path of two-dimensional truss structures in the mid and high-frequency domain, this paper proposed a fast dynamic calculation method—the impedance synthesis method (ISM)—which is based on an analytical equation with litter elements. Firstly, the global coordination vibration impedance of a Timoshenko beam truss is derived; Secondly, a dynamic model of a two-dimensional truss structure is built up with a single truss beam by force balance and geometric continuity; then, real and imaginary parts of dynamic responses and force in simple and periodically truss structures are verified by compared with FEM results, respectively; finally, the transfer path analysis (TPA) method is applied to separate the contribution of different transfer paths of power flow in periodical truss structures. The results show that the TPA method can easily find the line spectrum frequency of power flow, which should be considered in vibration control. This method can also be expanded to three-dimensional, honeycomb, and other truss beam structures.

Initiated by the problem of the coupled vibration of three-dimensional pipes conveying fluid, a spectral element method is proposed to address its dynamic characteristics. Based on a more comprehensive fluid-filled beam model than previous studies, not only the shear deformation, gravity, initial tension and fluid friction, but also the fluid–structure coupling is analyzed so as to obtain more reasonable results. The present method is validated by comparing numerical results of a T-shaped branched pipe with data from the literature, as well as from finite element software. It is shown that the spectral element method (SEM) has remarkable advantages over finite element method in computational efficiency and accuracy. In addition, through experiments on the vibrations of an L-shaped water-filled pipe, the in-plane and out-plane acceleration responses by SEM are also verified. This method would have great potential in modeling the vibrations of complex pipelines conveying fluid in a variety of engineering applications.

Dynamic vibration absorbers (DVAs) are often used to reduce vibrations in narrow frequency ranges. To reduce the flexural vibrations of a fluid-filled pipe system in a broader frequency band, several DVAs are attached to the pipe periodically to constitute a system akin to a locally resonant phononic crystal. Each DVA is analyzed based on mechanical impedance theory, and Bloch wave theory and the transfer matrix method are used to investigate the wave propagation in such a periodic system. The validity and accuracy of the natural frequencies and dynamic responses obtained are verified by comparing the present numerical results with results from the finite-element method. Also analyzed are the band-gap formation mechanism and how various system parameters influence the band-gap behavior, such as how the lattice and absorber properties influence the location and width of the lowest band gap. Lastly, a mass–spring DVA is designed and attached periodically to find the existence of locally resonant band gaps. The analytical and experimental results show that the mechanical impedance of the DVA is the main factor for the band-gap formation mechanism. When the DVAs are periodically arrayed, it can more effectively control flexural pipe vibration by broadening the bandwidth they attenuate and increase the magnitude of vibration attenuation.