Purpose <p>With the increasing demand for low-frequency vibration and noise control, achieving vibration attenuation in the low-frequency range remains a critical challenge.</p> Methods <p>The present study proposes several metamaterial beam configurations with embedded inerter-based units and systematically investigates dynamic characteristics. The transfer functions of oscillators in each configuration are derived using the Laplace transform, through which the necessary and sufficient conditions for ensuring oscillator stability are established. Finite element simulations are additionally carried out to characterize the transmission response and vibration attenuation capability of the finite acoustic metamaterial beam.</p> Results <p>The analysis reveals that increasing the damping ratio enhances energy dissipation within the passband and facilitates the merging of two adjacent band gaps into a single broadband gap. The effect of inerter distribution on dual-bandgap formation and low-frequency shifting is further elucidated. The influence of each parameter on the dispersion relation is evaluated by sensitivity analysis, and the key parameters governing wave propagation are identified and ranked. Furthermore, the nonlinear effects are quantified, and the influence of unit-cell locations on vibration attenuation and wave propagation is systematically evaluated.</p> Conclusions <p>Theoretical and numerical results demonstrate that incorporating an inerter modifies the resonance and anti-resonance characteristics, thereby generating dual band gaps in specific configurations. The left-side nonlinearity induces an ultra-low-frequency band gap initiating from 0 Hz, whereas the right-side nonlinearity gives rise to an ultra-broad continuous band gap, with the total bandwidth increased by 31.5%. These findings provide a viable solution for designing metamaterial capable of achieving low-frequency and broadband vibration suppression.</p>