We report a mechanical metamaterial-like behavior as a function of the micro/nanostructure of otherwise chemically identical aliphatic polyurea aerogels. Transmissibility varies dramatically with frequency in these aerogels. Broadband vibration mitigation is provided at low frequencies (500-1000 Hz) through self-assembly of locally resonant metastructures wherein polyurea microspheres are embedded in a polyurea web-like network. A micromechanical constitutive model based on a discrete element method is established to explain the vibration mitigation mechanism. Simulations confirm the metamaterial-like behavior with a negative dynamic material stiffness for the micro-metastructured aerogels in a much wider frequency range than the majority of previously reported locally resonant metamaterials.