Characteristic impedance and energy transmission through generalized damped 1D monocouple metamaterial

This study presents a comprehensive investigation of energy transmission in a generalized monocoupled one-dimensional metamaterial chain, termed the Inertial Amplifier Negative Mass Negative Stiffness (IANMNS) system, through both time-domain and frequency-domain analyses. While earlier studies have predominantly focused on frequency-domain responses of monoatomic or mass-in-mass chains, the present work extends the framework by incorporating time-domain energy transmission analysis to capture the full dynamics of wave propagation into the IANMNS system. The key novelties of this work are: (i) the introduction of damping into the impedance formulation, leading to a generalized impedance framework for damped discrete IANMNS systems, and (ii) a detailed characterization of energy distribution, i.e., kinetic, potential, and dissipative, within finite chains across both propagation and attenuation bands. The results demonstrate that in the attenuation band, energy is strongly localized and the transmission is suppressed by several orders of magnitude relative to the propagation band. Furthermore, the validity of the proposed impedance formulation is confirmed through spatiotemporal simulations, which illustrate the absence of spurious reflections at impedance-applied boundaries. Together, these contributions establish a rigorous and extended methodology for analyzing energy transmission in damped metamaterial systems, offering new insights for the design of advanced wave-control and vibration-suppression devices.