Graduate Student Research Assistant, University of Michigan
Distributed vibration absorbers used to find light-weight vibration suppression methods.
One common method to reduce vibrations in structures is to use a single large vibration absorber. This is typically a large mass connected to a pendulum or a spring. As the structure vibrates the large mass oscillates and absorbs the vibrations resulting in significantly reduced motion in the structure. This is an effective method but can add significant weight to the structure which is undesirable in aerospace structures. My research looks at using several small vibration absorbers distributed throughout the structure instead of a single large vibration absorber. We call any structure with distributed vibration absorbers, metastructures. This allows for greater flexibility in the design process and also provides more parameters to vary. Using distributed vibrations absorbers to suppress vibrations allows the structure to experience significant vibration reductions without adding additional weight to the structure.
Abstract: International Journal of Modern Physics B, Ahead of Print. In this paper, the low-frequency and tuning characteristic of band gap in a two-dimensional phononic crystal structure, consisting of a square array of aluminum cylindrical stubs deposited on both sides of a thin rubber plate with slit structure, are investigated. Using the finite element method, the dispersion relationships and power transmission spectra of this structure are calculated. In contrast to a typical phononic crystal without slit structure, the proposed slit structure shows band gaps at lower frequencies. The vibration modes of the band gap edges are analyzed to clarify the mechanism of the lowest band gaps. Additionally, the influence of the slit parameters and stub parameters on the band gaps in slit structure are investigated. The geometrical parameters of the slits and stubs were found to influence the band gaps; this is critical to understand for practical applications. These results will help in fabricating phononic crystal structures whose band frequency can be modulated at lower frequencies.
Pub.: 15 Sep '16, Pinned: 28 Jun '17
Abstract: Because effective material properties are essential concepts in the analyses of wave phenomena in metamaterials, they may also be utilized in the optimal design of metamaterials. In this work, we propose a topology optimization method directly using the Effective Mass Density (EMD) concept to maximize the first bandgaps of two-dimensional solid Locally Resonant Acoustic Metamaterials (LRAMs). When the first bandgap is characterized by the negative EMD, the bandgap maximization can be formulated efficiently as a topology optimization problem to broaden the frequency zone of the negative EMD values. In this work, EMD is calculated by considering the macroscopic isotropy of LRAMs in the long wavelength limit. To facilitate the analytical sensitivity analysis, we propose an elaborate calculation scheme of EMD. A sensitivity averaging technique is also suggested to guarantee the macroscopically isotropic behavior of the LRAMs. In the present study, the coating layer interfacing the core and the matrix of a ternary LRAM is chosen as the design region because it significantly influences the bandgap. By considering several numerical examples, the validity of this method is verified, and the effects of the mass constraint ratios on the optimized results are also investigated.
Pub.: 01 Aug '16, Pinned: 28 Jun '17
Abstract: Locally resonant metamaterials are characterized by bandgaps at wavelengths that are much larger than the lattice size, enabling low-frequency vibration attenuation. Typically, bandgap analyses and predictions rely on the assumption of traveling waves in an infinite medium, and do not take advantage of modal representations typically used for the analysis of the dynamic behavior of finite structures. Recently, we developed a method for understanding the locally resonant bandgap in uniform finite metamaterial beams using modal analysis. Here we extend that framework to general locally resonant metastructures with specified boundary conditions using a general operator formulation. Using this approach, along with the assumption of an infinite number of resonators tuned to the same frequency, the frequency range of the locally resonant bandgap is easily derived in closed form. Furthermore, the bandgap expression is shown to be the same regardless of the type of vibration problem under consideration, depending only on the added mass ratio and target frequency. It is shown that the number of resonators required for the bandgap to appear increases with the target frequency range, i.e. respective modal neighborhood. Furthermore, it is observed that there is an optimal, finite number of resonators which gives a bandgap that is wider than the infinite-absorber bandgap, and that the optimal number of resonators increases with target frequency and added mass ratio. As the number of resonators becomes sufficiently large, the bandgap converges to the derived infinite-absorber bandgap. The derived bandgap edge frequencies are shown to agree with results from dispersion analysis using the plane wave expansion method. Numerical and experimental investigations are performed regarding the effects of mass ratio, non-uniform spacing of resonators, and parameter variations among the resonators.
Pub.: 09 Dec '16, Pinned: 28 Jun '17
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