<p>The 3D vibration model of metaconcrete single aggregate is established under the linear elastic deformation. The soft coating and mortar are replaced by equivalent spring. Their equivalent mass, length and stiffness are calculated. The nonlinear control equation of free vibration is derived. The analytical expression of solution was acquired. A kind of method for solving such equation was given. The analytical expression of non-damping and damping nonlinear frequency are obtained. The effects of material parameters, geometrical parameters and initial conditions of aggregate on vibration were analyzed. The backbone curves of free vibration are studied. The influence of elastic modulus of soft coating on the backbone curves, the time history curve of displacement, etc. are investigated. The selection of aggregates is optimized. It can provide theoretical reference for engineering design such as designing aggregates attenuating high-frequency wave, low-frequency vibrations, etc. and for the theoretical study of multiple cells aggregate vibration.</p>