Broadband low-frequency sound insulation of a metamaterial plate with inertial amplification

The recent development of Inertia Amplification (IA) acoustic metamaterial (AMM) opens a new venue for insulating low-frequency sound waves. This differs from conventional approaches that rely excessively on the structural density of the insulator and, therefore, lead to prohibitively heavy structures. The IA-AMM acquires a large effective density and a broad flexural bandgap by amplifying the inertia of many small mass elements periodically distributed in its unit cells, thus holding great promise as an effective yet lightweight solution for low-frequency sound insulation. This paper explores this possibility through numerical and experimental in-vestigations. A semi-analytical model of an IA-AMM plate is developed by combining analytical equations characterizing the kinematics of an IA mechanism and FEM equations governing the vibration of the host plate. Based on this model, sound transmission characteristics of the plate under various sound incidences are analyzed with different amplification angles. By comparing with a locally resonant AMM plate, we found that the IA-AMM plate's sound transmission losses (STLs) are significantly and systematically improved over a wide frequency range of 116-544 Hz. To understand the underlying physics, the band diagram of the IA-AMM plate is calculated, which indicates the formation of a flexural bandgap covering the frequencies of the improved STL. The velocity contour of the plate at the center frequency of this bandgap also reveals much-suppressed vibration velocity amplitudes and a dipole-like sound radiation directivity, further explaining the observed enhancement of the sound insulation ability. Numerically predicted improvement of sound insulation is finally confirmed by experiments.