High contrast biphasic mechanical metafilter for elastic wave mitigation

The intrinsic composite microstructure of heterogeneous cellular media provides effective mechanisms for governing the propagation of elastic harmonic waves. The dispersion properties of biphasic two-dimensional phononic crystals, characterized by strong acoustic impedance contrast between the constituent phases, are investigated. Two microstructural configurations are considered: a native configuration with periodic inclusions embedded in a homogeneous matrix, and an engineered configuration obtained by introducing inclusion-connecting channels that enhance the intercellular connectivity. The biphasic medium is modeled as a classical non-dissipative solid continuum, governed by differential equations with phase-dependent piecewise coefficients. Methodologically, a hybrid semi-analytical finite element framework is employed to determine the Floquet–Bloch dispersion relations. Parametric analyses reveal how impedance contrast and geometrical connectivity influence the emergence and amplification of low-frequency bandgaps. Bandgap opening stems from different physical mechanisms: in the native configuration, large bandgaps emerge for increasing impedance contrast, whereas in the engineered configuration, large bandgaps arise for decreasing impedance contrast. The systematic investigation of the interplay between elastic properties and geometrical cell-shaping in tailoring the band structure of biphasic cellular media provides a unified framework for their spectral design. A design chart mapping the bandgap amplitude onto the principal mechanical parameters is provided to guide the development of high-performance metafilters. Finally, time- and frequency-domain analyses of finite periodic arrays under broadband excitation demonstrate the ability of the proposed configurations to attenuate elastic waves within the predicted bandgap ranges, which fall within the range of human sensitivity.