Pulse Shaping in 1D Elastic Waveguides for Shock Testing

Mechanical shock events can be reproduced in the laboratory using Hopkinson bar tests. These tests are used to qualify electronic systems exposed to these mechanical shocks by defining the shape of the pulse as a test specification. In these tests a projectile strikes an incident bar, creating a pulse which travels through the incident bar into the electronics system. The quality of these tests depends on how close the shape of the incident pulse is to the shape specified for the test. Pulse shapers are one way to accomplish this. These are typically inserts of various shapes and materials applied between the projectile and the incident bar. This paper introduces a new way to control the shape of the incoming pulse, through the use of elastic metamaterial concepts.

A variety of elastic metamaterial concepts have been developed to reduce or mitigate vibration in structures, create directional waves, or introduce edge modes which cause waves to follow predefined paths. Traditionally, bandgaps have been prioritized over global dispersion characteristics. In contrast, this paper examines four metamaterial concepts for their ability to change the shape of a typical input pulse, a haversine, propagating through a 1D wave guide. These four concepts include grounding springs, local resonators, Bragg scattering, and a continuously changing wave cross-section (e.g., horns). These concepts are then evaluated using a transfer matrix method to determine their effect on the wave dispersion, and on the output wave shape in the time domain. The results of the analysis show that metamaterial concepts are most effective when they are tuned to introduce dispersion or bandgaps near the fundamental frequency of the incident wave. Results further show that ground springs, which create high pass filters, have little effect on the wave shape other than attenuation since they typically are designed for frequencies much lower than the fundamental input frequency of a pulse. Bragg scattering can be used to increase the time duration and rise time of the wave. Local resonance can be used to increase the rise and fall time, but also leads to high amplitude distortion of the wave shape. Horns can be used to increase or decrease the wave amplitude while maintaining the wave duration. This paper also examines combinations of these different materials and their effects, using an optimization routine. In conclusion, by optimization of several concepts, pulse shapes can be tuned to adequately approximate desired wave shapes using metamaterial concepts.