Analysis Impact tests were initially conducted on the test fixture with no helmet on the head. A medium size modally tuned hammer (PCB 086D05) with a rubber tip was used. The head was impacted nine times at 42 different locations. A modified exponential window was applied to the time data to compensate for weakly damped low frequency responses due to the isolation table. The time history data was used to estimate the frequency response function in two ways providing H1 and H2. Both frequency response estimates are a function of the auto-power Gxx (Equation 1) and cross-power Gxy (Equation 2), which are calculated using Navg averages of the digitally sampled input (impulse hammer), Xi, and output (accelerometer response), Yi, frequency spectra measurements. The frequency response estimate H1 (Equation 3) is more accurate when there is little noise on the input, whereas H2 (Equation 4) is more accurate when there is little noise on the output. Gxx ω( )= Xi ω( )Xi * ω( ) i=1 Navg (1) Gxy ω( )= Xi ω( )Yi * ω( ) i=1 Navg (2) H1 ω( )= Gxy ω( ) Gxx ω( ) (3) H2 ω( )= Gyy ω( ) Gxy ω( ) (4) For the purposes of analysis and further data processing, the H1 estimator was the only estimator considered in this paper. The modal hammers used for the impact tests were tuned and were assumed to introduce less noise into the measurements than the noise observed in the output signal supplied by the accelerometers. 558
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