On two initial-boundary-value problems for impact dynamics of metaconcrete rods

Coated stiff sphere-filled metacomposites are a new type of composite materials for vibration isolation and wave attenuation. In the present paper, a continuum model is presented to study impact dynamics of coated stiff sphere-filled random metacomposite (called “metaconcrete”) rods. Compared to existing discrete and numerical models for metaconcretes, the present model is characterized by a single governing equation and enjoys mathematical simplicity and the generality. A transformation technique is used to change the original problem with a time-dependent end condition at the impacted end to an equivalent problem with two zero-end conditions, which makes it possible to solve the initial-boundary-value problem with Fourier-series method. The efficiency and accuracy of the present model are demonstrated by comparing its predicted results with known data, and several impact dynamic problems of metaconcrete rods beyond the existing literature are studied. The present model has the potential to be extended to 2D or 3D metaconcrete structures.