Formation of quasi-static stop band in a new one-dimensional metamaterial

The main objective of this paper is to propose a new metamaterial capable of generating a quasi-static stop band from zero frequency. The metamaterial is modeled by a lattice system made of mass-in-mass units. The unit cell of the proposed metamaterial contains a resonator connected to bar-spring mechanism embedded in a host mass and also linked to a fixed substrate. The stop band behavior of the new metamaterial is first investigated on basis of a lumped-parameter infinite lattice model. The equations of motion are derived using the Lagrangian approach, and then Bloch’s theorem is used to derive the dispersion relation. Analytical expressions of the stop band edge frequencies are derived in closed-form. The proposed metamaterial is then studied on a finite lattice model to verify the stop band behavior predicted using the infinite lattice model. A closed-form expression of the transmittance is derived using the matrix method. It is shown that there are two frequency regions in the transmittance spectrum of the finite chain in which the amplitude is considerably attenuated which correspond to the stop bands predicted in the dispersion curve of the infinite chain. Finally, a parametric study is performed to investigate the effects of various design parameters of the proposed metamaterial.