The frequency response, H1, was used to conduct modal analysis to determine the estimated mode shapes of the system. It is believed that mode shapes would be an effective means of understanding the differences in performance of one helmet relative to another helmet. Frequency responses are dependent on impact location and direction, e.g., the frequency response in the x direction is not the same as in the y or z direction due to the stiffnesses of the neck in these directions. As a result, each impact location may result in different modal frequencies and mode shapes dominating the dynamic response. For example, if the head is struck at location C7, which is largely in the x direction (Fig 2), the dominant modal frequency is 34.9 Hz. The modal shape corresponding with the placement of the three sensors (Fig 2) indicates that all three sensors move in the same direction. The head and neck deflect more than the table. In addition, the deflection of the head and neck are mostly in phase with the table, and only slightly out of phase with each other. In comparison, if the head is struck at R5, which is largely in the y direction (Fig 3), the dominant modal frequency is 10.4 Hz. The mode shape (Fig 3) is different than the one corresponding to the dominant modal frequency for an impact at C7. In addition, the head and neck are 180 degrees Fig 3 Modal response of the head-neck-table system, normalized by the table’s response, when the head is impacted in the y direction at R5 Fig 2 Modal response of the head-neck-table system, normalized by the table’s response, when head is impacted in the x direction at C7 559
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