Introducing and analyzing a periodic pipe-in-pipe model for broadband ultra-low-frequency vibration reduction in fluid-conveying pipes

A new model of periodic structure is proposed and analyzed. This structure is composed of an inner fluid-conveying pipe with periodic material arrangement carrying periodic arrays of outer cantilever pipes. The generalized differential quadrature rule (GDQR) method combined with the Bloch theorem is used to calculate the vibration band gaps of the structure. Results are verified by the forced vibration responses obtained using the GDQR method. Results indicate that the first two band gaps of the fluid-conveying pipe with periodic material arrangement can get close to each other and move to low frequency regions by changing the length of cantilever pipes. For high fluid velocity values in which the first band gap starts from zero frequency, since the second band is very close to the first band, this periodic structure can be used for vibration reduction over a wide band gap starting from zero frequency. Based on these results, it can be concluded that instead of increasing the total size of the periodic structure, these periodic arrays of cantilever pipes can be implemented to create a wide ultra-low-frequency band gap. Finally, verification of the GDQR method shows that it can be used as a precise numerical method for vibration analysis of the structures such as fluid-conveying pipes and moving belts.