On the elastic metamaterial with negative effective mass

Presented here is a theoretical study on basic subunits of the elastic metamaterial used for vibration and sound mitigation. The subunit of the material is modeled as a mass-in-mass two degree of freedom excited system where the mass-nonlinear spring system is used as a vibration absorber. The nonlinearity in the system is of power type and the excitation force is a general time-periodic function. The motion is described with two coupled second order nonlinear and nonhomogeneous equations. The novelty in the paper is the newly developed analytical procedure for approximate calculation of the response of a power-type nonlinear coupled conservative and non-conservative two degree-of-freedom system subjected to generally time-periodic forcing given in the form of the Ateb function. In addition, based on the known concept of 'effective mass' for the linear vibration absorber, the 'effective mass' for the nonlinear vibration absorber is developed. It is obtained that the effective frequency bandwidth for the suggested nonlinear mass-in-mass system is much larger than for the linear one. For the nonlinear system the frequency stop-band area of vibration tends to be continual. The results are proved numerically and experimentally.