Sound transmission of acoustic metamaterial beams with periodic inertial amplification mechanisms

Abstract This paper presents the improved sound insulation performance obtained from a new type of acoustic metamaterial, built by attaching periodic inertial amplification (IA) mechanisms to a host beam. The IA mechanism is a triangular bar-and-hinge device, which connects a small mass to the host beam at two separate locations. The band structure of a unit-cell and the Sound Transmission Loss (STL) of a finite-length beam are calculated by the spectral element method (SEM), which are validated against finite element references. Numerical simulations show that the STL of the IA acoustic metamaterial beam outperforms that of an ordinary beam across a wide band starting from a very low frequency, which suggests the low-frequency soundproof capacity of the IA acoustic metamaterial beam is greatly enhanced. However, the STL curve also experiences a sudden fall after that band, causing an undesired sound insulation valley. To reveal the underlying physics, the band diagram of the beam is studied together with the trace wavenumber of the incident sound wave. It is found that, due to the collectively amplified inertia of periodic small masses, a wide bandgap is introduced in the band diagram at low frequencies, which effectively suppresses flexural vibration of the beam and eventually leads to the observed STL enhancements. However, as a consequence of this bandgap, band diagram inevitably intersects with acoustic trace wavenumber, creating a coincidence phenomenon. Although happens earlier than classical coincidence, this new coincidence produces a similar STL valley. To mitigate this drawback, a hybrid unit-cell containing two IA mechanisms is designed, which attempts to cover the valley caused by one mechanism with the bandgap induced by the other. The effectiveness of this new design is verified and discussed at last.