Complex Dynamic Mass Density in Acoustic Metamaterials

The mass density of normal acoustic materials is usually a real number. Energy dissipation is induced by the volume or shape change of the materials, which relates to the imaginary parts of complex moduli. Here, we show that by using acoustic metamaterials, complex dynamic mass density can also be realized. In this case, energy dissipation is induced by the change of momentum of the material. We analyze the physical origin of such complex mass density and provide a theoretical approach to calculate the effective complex dynamic mass density for acoustic metamaterials with dissipation. The obtained effective complex mass density is verified by finite element simulations, including both transmission studies and realization of coherent perfect absorption. Our work shows a way to realize complex mass density, which has important applications in enhancing absorption of acoustic waves.