Combining lightweight characteristics with favourable noise and vibration behaviour, locally resonant metamaterials with vibro-acoustic stopband behaviour are gaining increasingly more attention. In view of applicability of metamaterials, this paper investigates the effects of curvature on stopband behaviour. Through derivation of curved unit cell models, dispersion curves for cylindrically curved infinite periodic structures are derived. The effect of curvature on metamaterials is investigated through both an academic example of an infinite cylindrically curved panel with added spring-mass systems and a realizable curved panel with resonant structures. It is shown that, whenever pure flexural motion exists in the host structure, the stopband mechanism can be applied to achieve flexural stopbands.
This paper investigates a metamaterial solution for efficient vibration attenuation and acoustic radiation reduction of an aluminum pipe. To this end, using unit cell predictions, locally resonant structures are designed to have a pronounced flexural resonance frequency at the vicinity of a dominant vibration mode of the pipe. A direct approach of the Bloch-Floquet theorem is adopted to provide the dispersion relation representing wave motion in an infinite metamaterial pipe. Using these wave dispersion relations, the frequency range of the stopband zone created by the metamaterial solution is predicted. The dynamic behavior of the finite counterpart is predicted using the Finite Element Method (FEM). The resonant structures are produced from polymethyl methacrylate (PMMA) panels and are added to the host structure. In order to properly characterize both the vibrational behavior of the metamaterial pipe and the acoustic radiation from its wall, impact tests using roving hammer technique is performed on the pipe and both accelerations and acoustic pressures are measured at different locations. The experimental results show a pronounced stopband zone created by the addition of a few rows of resonant structures. Moreover, comparisons between the measurements and numerical predictions show a good agreement.
A bi-level operation scheduling of distribution system operator (DSO) and multi-microgrids (MMGs) considering both the wholesale market and retail market is presented in this paper. To this end, the upper-level optimization problem minimizes the total costs from DSO’s point of view, while the profits of microgrids (MGs) are maximized in the lower-level optimization problem. Besides, a scenario-based stochastic programming framework using the heuristic moment matching (HMM) method is developed to tackle the uncertain nature of the problem. In this regard, the HMM technique is employed to model the scenario matrix with a reduced number of scenarios, which is effectively suitable to achieve the correlations among uncertainties. In order to solve the proposed non-linear bi-level model, Karush–Kuhn–Tucker (KKT) optimality conditions and linearization techniques are employed to transform the bi-level problem into a single-level mixed-integer linear programming (MILP) optimization problem. The effectiveness of the proposed model is demonstrated on a real-test MMG system.
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