Effective mass density of rigid sphere-reinforced elastic composites

An analytical model is presented to study metaelastic dynamic behaviors of rigid sphere-reinforced elastic random composites. The model is based on the concept that the deviation of the displacement field of embedded rigid spheres from the displacement field of the composite is responsible for novel metaelastic dynamic behaviors of stiff sphere-reinforced composites. Compared to the existing models, the present model offers a simple general method to analyze various 3D metaelastic dynamic problems of rigid sphere-reinforced random composites, and its validity and efficiency are demonstrated by comparing the predicted results with known experimental or numerical data on several typical steel/glass/lead-polymer composites. Several basic dynamic problems of rigid sphere-reinforced composite beams and rods are investigated, and some metaelastic dynamic phenomena (such as vibration isolation, localized buckling, and natural frequency within the bandgap caused by an attached concentrated mass) of stiff sphere-reinforced composites are demonstrated.