Phononic Materials for Pulse Shaping in Elastic Waveguides Motivated by Shock Testing

Mechanical shock events experienced by electronic systems can be reproduced in the laboratory using Hopkinson bar tests. In such tests a projectile strikes a rod, creating a pulse which then travels into the electronic system. The quality of these tests depends on the closeness of the shape of the incident pulse to a desired shape specified for each test. This paper introduces a new approach for controlling the shape of the incident pulse through the use of phononic material concepts, thereby improving the test procedure. Two dispersion-modifying concepts, phononic crystals and local resonators, are examined for their wave shaping capabilities in one-dimensional elastic waveguides. They are evaluated using a transfer matrix method to determine the output pulse shape in the time domain. Parametric studies show that no single parameter allows for precise-enough control to achieve the possible desired output pulse shapes. Instead, the parameters of an approximate, discrete model for a combined phononic crystal/locally resonant system are optimized together to achieve the desired pulse shape. A sensitivity analysis documents that the pulse shape is relatively insensitive to errors in the optimized parameter values. The optimized discrete model is then translated into a physical design, which when analyzed using the finite element method shows that desired pulse shapes are indeed produced.