Sound Transmission Loss of One-Dimensional Systems Containing Fictitious Metamaterials
* Presenting author
Metamaterials are distinguished from "normal" materials by unusual properties. Some behave as if the mass density or some elastic modulus were negative. However, in "real metamaterials" such unusual properties appear in limited frequency ranges only. Moreover, these properties are as a rule complex-valued, i.e. implicate damping, and depend on frequency. By contrast, the properties of "fictitious metamaterials" may be defined arbitrarily, regardless of physical realizations. Analytical studies of simple cases with frequency-independent negative mass densities and elastic moduli lead - via the transfer-matrix method - to instructive findings. The sound transmission loss of a mass-spring-mass system is optimal, if the spring constant is positive and both masses are equal and negative, or if the spring constant is negative and both masses are equal and positive. The transmission loss of a homogeneous one-dimensional elastic layer, which may be regarded as a generalization of a rigid mass or a massless spring, shows similar symmetries. With respect to the signs of the elastic modulus and the mass density the transmission loss depends only on the product of the two signs, i.e. on whether the signs are equal or different. Corresponding results are obtained for an elastic layer sandwiched between two rigid masses.