Metamaterial Applications for Vibration and Wave Propagation in 1D Elastic Rods

Abstract

The field of elastic metamaterials has experienced a large amount of development and is reaching a level of maturity where practical applications can be developed. This dissertation is focused on the application of elastic metamaterials and phononic crystals to problems encountered in industry. To this end, three applied problems are addressed: the vibration mitigation of a large electrical generator; the impact and bouncing of circuit breaker electrodes; and the use of phononic materials for pulse shaping in Hopkinson bar tests.

Various base isolation techniques have been developed for heavy machinery. This dissertation looks at the problem of a vibrating electric generator and how phononic material concepts could be applied to mitigate vibrations. Two concepts are investigated: the first uses resonators tuned to the motion and natural frequency of the mode closest to the excitation frequency; the second technique replaces the previous support with periodically applied grounding springs. The frequency response obtained using both techniques show that they can attenuate the response at the excitation frequency. Finally, a practical implementation of grounding springs is presented.

High voltage vacuum circuit breakers have become the standard for industrial circuit breaker applications. Circuit breakers interrupt the flow of electricity through an electrical network, protecting it if the current flow becomes too high. When the electrodes in a circuit breaker close, initiating the flow of electricity, they bounce off of each other before reaching resting contact. During bouncing arcing occurs between the electrodes, which can lead to permanent welding of the electrodes and failure of the circuit breaker. Previously, the electrode bouncing problem has been studied using discrete lumped element models, with the underlying assumption that the bouncing was arising from resonance within the system. However, this perspective ignores wave propagation when impact occurs. Herein a new model of electrode bouncing, treating the electrodes as a continuous system, is developed. The model shows how waves propagate through the bouncing electrode system, and helps illustrate what parameters control the bounce time. Wave bounce criteria are also suggested which could help reduce circuit breaker bouncing.

Hopkinson bar tests are used to obtain dynamic material properties such as strain rate dependent stress-strain relationships. This is accomplished by sending a mechanical shock wave, or pulse, down the bar and into the material sample to be tested. Parameters such as amplitude, shape, and duration of the wave are important in obtaining the desired material properties. The research presented herein shows that through using optimized elastic metamaterial concepts, an input pulse to a longitudinal bar can be shaped to sufficiently approximate a specified, predefined output pulse. Concepts including local resonators, phononic crystals, grounding springs, and cross-sectional variations were investigated. These concepts are applied to a homogeneous rod and analyzed using the transfer matrix technique. The output of a metamaterial rod is predicted using the dynamic stiffness matrix. The metamaterial parameters for a combined phononic crystal - local resonator are then tuned using an optimization algorithm to achieve the desired response of the system.

These applications demonstrate three scenarios where phononic materials can be applied to industrial problems, for vibration mitigation and pulse shaping. The generator vibration mitigation problem investigates phononic material techniques that would maintain the static stiffness required to support the generator. The circuit breaker problem develops a new model for bouncing that clarifies the role of wave propagation, suggesting that phononic materials could be used to modify the wave shape in a beneficial way. The Hopkinson bar problem, which had similarities to the circuit breaker problem, develops this concept further, resulting in pulse shaping using phononic materials. This is a novel application.