Sound transmission loss through metamaterial plate with lateral local resonators in the presence of external mean flow

In the context of sound incident upon a metamaterial plate, explicit formulas for sound transmission loss (STL) are derived in the presence of external mean flow. Metamaterial plate, consisting of homogeneous plate and lateral local resonators (LLRs), is homogenized by using effective medium method to obtain the effective mass density and facilitate the calculation of STL. Results show that (a) vigorously oscillating LLRs lead to higher STL compared with bare plate, (b) increasing Mach number of the external mean flow helps obtain higher STL below the coincidence frequency but decreases STL above the coincidence frequency due to the added mass effect of light fluid loading and aerodynamic damping effect, (c) the coincidence frequency shifts to higher frequency range for the refracted effect of the external mean flow. However, effects of the flow on STL within negative mass density range can be neglected because of the lateral local resonance occurring. Moreover, hysteretic damping from metamaterial can only smooth the transmission curves by lowering higher peaks and filling dips. Effects of incident angles on STL are also examined. It is demonstrated that increasing elevation angle can improve the sound insulation, while the azimuth angle does not.