Inner resonance in fiber-matrix composites with homogeneous fibers

Abstract

The microstructure of elastic composite materials can be adjusted in order to provide inner resonance, leading to negative dynamic density. In a first step, the results on the process using asymptotic expansion that provides the structure of the effective behaviour and the scaling of physical parameters leading to inner resonance are recalled. The process allows to describe the dynamic localization problem that must be considered in order to provide the effective behaviour. The localization problem is solved for elastic composites containing cylindrical fibers with circular cross-section. It involves the recovering of eigenfrequencies of a cylindrical domain through Bessel functions. While there are several sets of eigenfrequencies, it will be shown that only one set of eigenfrequencies contributes to the dynamic density. The eigenfrequencies and the participation factors for each resonance are provided, leading to a full description of the dynamic density.