Novel metamaterial concepts can be used to economically reduce flexural vibrations in coupled piperack systems. Here, we model pipe on flexible supports as periodic systems and formulate dispersion relations using Floquet-Bloch theory which is verified by a finite element model. Owing to the flexibility of the coupled system, a narrow pass band is created in low frequency regime, in contrast to the case of pipe without any rack. Two types of vibration reduction mechanisms are investigated for pipe with different supports, i.e. simple and elastic support. In order to tune the band gap behaviour, lateral localized resonators are attached at the centre of each unit cell; conversely, the lateral distributed resonators are realized with a secondary pipe existing in the system. The results reveal that both Bragg and resonance type band gaps coexist in piping systems due to the presence of spatial periodicity and local resonance. Although, the response attenuation of a coupled pipe-rack system with distributed resonators is found to be little lower than the case with the localized one, the relatively low stiffness and damping values lead to cheaper solutions. Therefore, the proposed concept of distributed resonators represents a promising application in piping, power and process industries. Pipes conveying fluid supported in equally spaced racks are very common in liquefied natural gas (LNG) plants, thermal power plants, petroleum industries, chemical plants and in many other engineering applications. LNG plant consists of many units such as gas receiving terminals, pipelines, storage tanks, etc. Long pipelines in such plants are used to carry refrigerated liquefied gas to storage tanks and shipping terminals. Excessive vibrations of pipelines due to ambient load, flow pulsation, valve or support excitation can result in fatigue damage, loosening of connections, etc., which may lead to fire, explosion, safety and environmental issues. It is thus essential to protect them from large vibration amplitude. To crystallize the idea, an LNG plant containing a coupled pipe-rack system connected to a tank 1 is shown in Fig. 1a. Such a system usually contains pipes of different dimensions supported on a finite periodic rack as highlighted in Fig. 1b. Periodic structures have been used as a common tool for mitigation of acoustic and elastic waves over the past decades 2-5. Periodicity in a structure may be in one, two or in all the three dimensions 6. Such systems exhibit unique frequency band gap characteristics 3 , which can be generated either due to the Bragg scattering 6,7 or by local resonances 8. As a result, they allow only waves of a certain frequencies to pass through, which are represented as pass or propagation bands. The remaining frequencies get attenuated, thereby forming stop or non-propagation bands. If the spatial periodicity of a structure is comparable to the wavelength λ, then Bragg band gaps are induced in the structure and appear around the frequencies governed by the Bragg condition = = … λ () l n n , where...

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Periodic structures possess frequency bandgaps wherein the waves cannot pass through. Here, the propagation behaviour of vertical and lateral flexural waves and its control in a railway track supported on periodic sleeper blocks connected using fasteners is investigated. The dispersion relationships for two kinds of waves are derived through Floquet–Bloch theorem, and the ensuing band structures are validated from finite element (FE) models. The results demonstrate that a Bragg and a locally resonant (LR) bandgap evolve in the track for both types of waves in the examined frequency range. However, the bandwidth of these bandgaps is found to be very small. Thus, waves can freely propagate in the track for a large frequency range, causing vibration and noise. Subsequently, the dependence of transmission properties of waves on the number of unit cells is studied. It is observed that the attenuation in the bandgap is significantly improved on increasing the number of unit cells. Further, to tune the bandgap properties, a single-degree-of-freedom resonator (SDoF) is used in the middle of each unit cell of the track. Afterwards, the parametric influence of resonator properties, that is, mass, stiffness and damping, on bandgaps is investigated in depth. Moreover, the phenomenon of bandgaps coupling is demonstrated when the resonator is tuned near the Bragg bandgap. The results provided herein are promising to realize the characteristics of flexural waves and to design resonators for track structures.

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