Logarithmic scaling law of broadband acoustic transmission in compressed core-shell granular metamaterials

Conventional static acoustic materials struggle to adapt to complex environments with varying loads. While granular media possess the potential for pressure-sensitive tuning due to their adjustable contact stiffness, their acoustic responses are often unstable due to interfacial micro-slips and energy dissipation. In this study, a pressure-sensitive acoustic metamaterial based on a metal-core and ceramic-shell structure was designed and fabricated to achieve stable, dynamic control of broadband acoustic energy. A step-loading ultrasonic transmission system was established to evaluate the acoustic evolution within a pressure range of 0.25 to 2.5 MPa. Experimental results confirm that the transmitted acoustic energy follows a robust logarithmic scaling law. Specifically, within the 10 to 40 kHz effective band, the band-integrated power exhibits a high linear correlation with the logarithm of the pre-pressure, achieving a Pearson correlation coefficient exceeding 0.99. Mechanism analysis reveals that the dense barium titanate shell effectively eliminates stray interference caused by random micro-slips. This spectral smoothing effect reduces the normalized total variation by up to 53 percent and triggers a pressure-sensitive locking effect in high-frequency regions above 60 kHz. Simultaneously, the high-stiffness core significantly amplifies the evolution gradient of the pressure-sensitive response. This core-shell design successfully transforms stochastic discrete contact mechanics into stable metamaterial characteristics, providing a novel pathway for the development of adaptive broadband vibration-damping devices and high-sensitivity acoustic sensors under complex loading conditions.