An inerter-based concept of locally resonant fluid-conveying pipe

Preventing damage or failure caused by vibrations in periodic fluid-conveying pipes needs appropriate mitigation strategies. This paper proposes a novel concept of locally resonant fluid-conveying pipe resting on periodically spaced inerter-based resonant supports, each including an inerter and linear springs. On adopting a Timoshenko beam model for the pipe, two types of inerter-based resonant supports are investigated, differing by the arrangement of the internal components, i.e., inerter and springs. For both types, elastic wave dispersion analyses of the infinite pipe demonstrate the existence of two low-frequency band gaps in the frequency response. The second band gap, caused by local resonance, exhibits better attenuation over a relevant part of its frequency range; its lower/upper edge frequencies and amplitude may be suitably changed depending on the parameters of the inerter-based resonant supports, and very considerable amplitudes can be obtained thanks to the large inertia effects warranted by the grounded inerter. The influence on the band gaps of key parameters such as fluid velocity and ratio of fluid mass to total pipe mass is assessed. Moreover, the effect of damping is considered, assuming a Kelvin–Voigt viscoelastic behavior for the pipe material and including viscous dashpots in parallel with the springs within the inerter-based resonant supports. An original exact dynamic-stiffness method is formulated for computational purposes, targeting wave dispersion analysis of the infinite pipe as well as frequency-domain analysis of the finite pipe. In particular, the main novelty is the derivation of the exact dynamic-stiffness matrix and exact load vector of the unit cell of the Timoshenko pipe with Kelvin–Voigt viscoelastic behavior. Remarkably, the transmittance of the finite pipe confirms the predictions from wave dispersion analysis of the infinite pipe and substantiates the effectiveness of the proposed concept of locally resonant fluid-conveying pipe.