Nonlinear acoustic metamaterial for efficient frequency down-conversion

Frequency conversion is one of the most important nonlinear wave phenomena that has been widely used in the field of electromagnetic waves for changing signal frequencies. Recently, studies on frequency conversion have been actively performed in the field of acoustics owing to its importance in nonlinear ultrasonic nondestructive evaluation and directional speakers. However, acoustic frequency conversion presents relatively poor efficiency owing to the small amplitudes of the converted frequencies and undesired intermodulation. Herein, we propose an acoustic metamaterial to achieve an efficient frequency down-conversion of acoustic waves. Based on background theory, we discovered that the amplitudes of the converted frequencies are inversely proportional to the cube of the speed of sound. Accordingly, we amplify the converted frequency components by reducing the effective speed of sound by coiling up space while suppressing undesired intermodulation by the Bragg gap. Numerical simulation and analytical results show that efficient frequency down-conversion is possible using the corresponding metamaterial. Additionally, dissipation due to viscosity and boundary layer effects is considered. We expect our study results to facilitate research regarding acoustic frequency conversion.