Wave propagation in a nonlocal supercell with lumped and distributed masses

This paper develops and analyzes a nonlocal supercell model for wave propagation in one-dimensional periodic chains that incorporates lumped and distributed masses together with beyond-nearest-neighbor couplings. The formulation advances earlier treatments of nonlocal metasurfaces by explicitly integrating distributed inertia, diatomic asymmetry, and long-range elastic links within a single supercell. The Bloch–Floquet theory is applied to the infinite chain to derive dispersion relations, while a complementary finite-chain formulation establishes the corresponding transmittance spectra. Parametric sweeps reveal how variations in mass ratios, stiffness asymmetry, and nonlocal coupling parameters govern the location, width, and attenuation characteristics of the spectral response. The results show consistent alignment between infinite- and finite-chain analyses, confirming that the proposed framework captures essential dynamic behavior across different structural scales. This unified treatment provides clear design guidance for engineering periodic media with tailored wave transmission properties and establishes a tractable foundation for the development of metamaterial structures aimed at vibration isolation, acoustic manipulation, and broadband attenuation.