A pinboard by
Katherine Reichl

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.


A General Theory for Bandgap Estimation in Locally Resonant Metastructures

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