Vibration Control of Periodically Supported Pipes Employing Optimally Designed Dampers

Vibration in periodic piping structures requires efficient attenuation measures. Structures composed of periodically arranged identical units show distinct bandgap characteristics, wherein waves and vibrations of particular frequencies cannot pass through. Along this vein, a pipe supported periodically on a rack structure is analyzed to determine the flexural wave propagation characteristics and thereby to design vibration control strategies. To understand the influence of stiffness of the rack on wave propagation, two models are examined; (i) pipe supported on a rack and (ii) pipe without rack. The relevant dispersion relations for both the cases are derived by means of Floquet-Bloch theory and the resulting bandgaps are validated using FE models. The results show that resonance and Bragg type bandgaps emerge in the pipe due to the existence of local resonance and spatial periodicity. The dependence of the propagation characteristics on the number of unit-cells is then investigated. It is found that attenuation within the bandgaps is significantly enhanced with an increase in the number of unit-cells. Further, to control two specific frequency ranges within a particular passband, two single-degree-of-freedom (SDoF) localized mass dampers (LMDs) are attached to the center of each unit-cell of the pipe. The LMDs are provided with identical mass ratios and are designed using a genetic algorithm (GA) based optimization for both the models. As an alternative to the LMDs, a novel possibility of using already existing pipes of smaller cross-sections in the rack as distributed mass dampers (DMDs) are evaluated. For identical mass ratios, the performance of LMDs was found to be higher than the DMDs. However, the latter represents a new, cost-effective and promising technique for vibration mitigation. Further, the effectiveness of both the LMDs and DMDs is verified by applying a Gaussian white noise as input. The findings of this paper are not only limited to pipelines, but can be applied when similar periodic beam structures are present in the system such as railway tracks, bridges resting on piers, etc.