Modeling shock attenuation in hydrogels via frequency-dependent acoustic drag

A new method for assimilating a frequency-dependent drag coefficient into time-domain acoustic simulations is presented. The method combines structural (wave propagation) simulations together with acoustic attenuation of the individual frequencies through a model for the frequency-dependent drag coefficient. An incident pressure pulse is obtained experimentally or from a preliminary finite element simulation. This pulse is then decomposed into its spectral components. The propagation of each frequency component is simulated separately with the appropriate drag coefficient. In the final stage, the nodal pressure for all single frequency simulations are summed to reconstruct the transmitted attenuated pressure pulse. This method is demonstrated using a previously calibrated spectral model of the attenuation of methyl cellulose hydrogel, but it can be used for any other damping material for which a frequency response function can be obtained.