A simplified metaelastic model for coated sphere-filled random composites

Abstract

A simplified metaelastic model is presented to study long-wavelength dynamics of random composites filled with coated rigid spheres under the condition that the characteristic wavelength of the displacement field is much larger than the average distance between adjacent coated rigid spheres. The model is characterized by a simple differential relation between the displacement field of the composite and the displacement field of the mass center of a representative unit cell. The validity and accuracy of the model are demonstrated by comparing its predicted bandgap frequencies with known numerical and experimental data. The efficiency and merits of the model are demonstrated by applying it to study vibration isolation of coated rigid sphere-filled composite rods and (periodic or non-periodic) free vibration caused by initial displacement or velocity disturbance of the embedded rigid spheres inside an otherwise static composite rod. The proposed model could offer a simple method to study various long-wavelength metaelastic dynamic problems of coated rigid sphere-filled random composites.