Abstract This work presents an analytical investigation of the free radial vibration of solid and hollow spherical bodies composed of heavy hard sphere–filled elastic metacomposites. Focusing on spherically symmetric vibration modes, the governing equations of motion are formulated in terms of the effective Lamé constants of the metacomposite medium while accounting for the dynamic interaction between the embedded heavy hard spheres as local resonators and the surrounding matrix. Closed-form solutions are derived using spherical Bessel functions and are extended to accommodate various boundary conditions. The resulting frequency equations are employed to study the influence of boundary conditions, geometric parameters, and the radius ratio of the sphere to the embedded hard spherical particles on the dimensionless natural frequencies. The analysis reveals that increasing the radius ratio systematically reduces the natural frequencies, while all natural frequencies are located in two separate ranges below and above the locally resonant bandgap, respectively. Furthermore, a pronounced clustering of natural frequencies is observed as the frequency approaches the lower bound of the bandgap, indicating a significant increase in the modal density. The proposed analytical framework provides explicit solutions without resorting to complex numerical procedures and offers new physical insights into the vibration behavior of metacomposite spherical structures, which are essentially different than the well-known free radial vibration of spherical elastic bodies and have not previously been reported in the literature.
Aghdam et al. (Mon,) studied this question.