Determination of effective mass density and modulus for resonant metamaterials

This work presents a method to determine the effective dynamic properties of resonant metamaterials. The longitudinal vibration of a rod with periodically attached oscillators was predicted using wave propagation analysis. The effective mass density and modulus were determined from the transfer function of vibration responses. Predictions of these effective properties compared favorably with laboratory measurements. While the effective mass density showed significant frequency dependent variation near the natural frequency of the oscillators, the elastic modulus was largely unchanged for the setup considered in this study. The effective mass density became complex-numbered when the spring element of the oscillator was viscoelastic. As the real part of the effective mass density became negative, the propagating wavenumber components disappeared, and vibration transmission through the metamaterial was prohibited. The proposed method provides a consistent approach for evaluating the effective parameters of resonant metamaterials using a small number of vibration measurements.