The Kelvin-Voigt (K-V) and the fluid TBI models both predict that when a head is close to the resting point at the end of a uni-directional rotational acceleration/deceleration pulse, the brain matter has a tendency to move in a circular way in the opposite direction with respect to the (sub)domain's boundary motion. Consequently, reversing the rotational direction increases the velocity induced in the brain matter relative to the skull, i.e., a resonance effect appears. The resonance effect is the most pronounced in the K-V model during rotations about the head's center of mass (bottom versus top panels). Shortening the period of the rotational pulses enhances the resonance effect, especially in the nonlinear fluid TBI model. A higher brain matter velocity usually leads to higher strain norm values. Although repetitive bi-directional rotations of the head do not further increase the velocity magnitudes, high strain resonance values are repeatedly created in the same brain locations enhancing the TBI severity/likelihood. Thus, the resonance effect may explain why repetitive shaking of a baby (cf. the Shaken Baby Syndrome) or repetitive blows to both sides of a boxer's head sometimes result in a severe brain injury even though, according to existing brain injury tolerance criteria, each uni-directional head motion should be harmless.