analysis and responses considered here were obtained using the small modal impact hammer. The size and shape of the helmets allowed for more impact points to be applied. Both helmets were impacted at approximately 100 impact locations with five impacts per impact point (Navg=5). The modal analysis conducted on the head was also conducted on the helmets. The dominate modes of the CMIF for each helmet can be compared. The dominant CMIF modes of the first helmet tested (ARL1) are similar for all sensor degrees of freedom (Fig 5). The three helmet sensors and the head, neck, and table sensor degrees of freedom all exhibit similar responses. The dominant CMIF modes of ARL1 suggest the helmet, head, neck, and table are strongly coupled. In addition, all sensors appear to have approximately the same amount of spectral energy (area under the CMIF spectrum). In comparison, the dominant CMIF modes of the second helmet tested (ARL3) are different for the sensor degrees of freedom (Fig 6). The responses of the helmet sensors are slightly similar; however, they are significantly different than the head, neck, and table sensors. As in the case of the ARL1 helmet, ARL3 exhibits coupling between the head, neck, and table. However, ARL3 is only coupled at particular frequency ranges where the dominant modes are closely spaced. Conversely, the frequency ranges where the modes are clearly separated correspond with uncoupled modes of vibration. In addition, the response magnitudes of the head, neck, and table are less, if not an order of magnitude less, than the helmet sensors. The lower response magnitude indicates less force and energy are experienced by the head, neck, and table. The CMIF suggests that ARL3 is a more effective helmet from a standpoint of low energy dynamic absorption compared with ARL1, because the ARL3 absorbs more energy than ARL1. Another method to determine the effectiveness of a helmet is to calculate the transmissibility of the helmet (as observed by the sensors placed on the helmet) to the head. The transmissibility (force, displacement, velocity, acceleration) is a function of the frequency response for the output and input degrees of freedom (Equation 6). For example, the transmissibility of the helmet to the head is a function of the output (the frequency response of the head) and the input (the frequency response of the helmet). Since the transmissibility is a ratio, if the transmissibility is greater than one, the output experiences more dynamic force than the input: the force is amplified. Conversely, if it is less than one the output experiences less dynamic force than the input: the force is attenuated. in out H H Tr 2 1 = (6) For every pair of frequency response functions, there is a corresponding transmissibility function. Therefore, two aggregate methods were developed to compare helmet transmissibilities: aggregate mean (AM) transmissibility and impact location average (ILA) transmissibility. The AM transmissibility is determined by calculating the mean cross-power and auto-power and using the results to calculate the mean frequency responses. The AM transmissibility provides a transmissibility function dependent on frequency. Therefore, plots can be created for each direction of each helmet sensor over the frequency range of interest. It is useful to focus on specific frequency ranges where the helmet amplifies or absorbs the force to the head. The AM transmissibility of ARL1 (Fig 7) confirms the analysis of the dominant CMIF modes of ARL1: the helmet does not significantly amplify or absorb force applied to the helmet. The AM transmissibility remains relatively close to one, neither significantly absorbing nor amplifying the force applied to the helmet. In comparison, the AM transmissibility of ARL3 (Fig 8) drops significantly less than one; this indicates the helmet absorbs force. However, the AM transmissibility in the y direction has several frequency ranges where the transmissibility is significantly greater than one. This indicates force applied to the helmet is amplified to the head for those specific frequency ranges. The amplification caused by ARL3 is significantly greater than any amplification caused by ARL1. The ILA transmissibility aggregate tool provides similar insight but from a different approach. The ILA transmissibility is calculated by normalizing the integral of the transmissibility function by the frequency range. Essentially the ILA transmissibility is the average transmissibility. Therefore, the ILA transmissibility is calculated for each impact location and sensor direction. The ILA transmissibility aggregate tool is an array of single values; if a value is greater than one, then on average force is amplified – if it is less than one, force is absorbed. The ILA transmissibility of ARL1 (Fig 9) indicates, on average, force is amplified from the helmet to the head, particularly in the x and y directions. In comparison, the ILA transmissibility of ARL3 (Fig 10) indicates, on average, force is absorbed by the helmet. It is interesting to note the ILA for both helmets indicates force in the z direction is always absorbed. This is most likely caused by the boundary conditions. In particular, the neck, as well as the isolation table, is stiffer in the z direction than the x or y direction. 562
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