Towards bandgap widening through beam-based coupling in mass–spring chains

This study investigates wave attenuation in a bi-coupled periodic chain composed of two unequal masses interconnected through beam elements and longitudinal springs. The baseline configuration is first examined to characterize its inherent dispersion behavior. To enhance its attenuation performance, diagonal springs are introduced between non-adjacent nodes, and their influence is evaluated through a spectral element formulation. Dispersion analysis based on the invariance-plane approach and complex wavenumber evolution shows that a single diagonal spring produces a distinct Bragg-type attenuation band, whereas incorporating two diagonal springs fundamentally alters the dispersion topology by inducing branch merging and the formation of a fully complex band. This geometric coupling mechanism results in a substantial widening of the attenuation region. Frequency–response functions computed for finite chains, and validated through numerical simulation and experimental measurements, confirm the transition from dual propagating modes to mixed propagation–attenuation behavior and ultimately to complete evanescence. Parametric studies reveal that increasing the diagonal stiffness from (Formula presented) to (Formula presented) N/m widens the bandgap by approximately 60% in the single-spring configuration and nearly 80% in the dual-spring system; variations in mass ratio produce comparable trends, while beam-width changes primarily shift the bandgap location. Collectively, the analytical, numerical, and experimental results establish diagonal geometric coupling as a robust and previously unreported strategy for tunable broadband vibration suppression in periodic mechanical systems.