Wave dispersion in one-dimensional periodic graded metacomposites

This paper reports on a theoretical model of one-dimensional (1D) periodic graded metacomposites for investigating and enlarging the bandgaps in which wave propagation is not allowed. The unit-cell of the acoustic metamaterial consists of external mass, spring and internal mass. Different from the conventional infinite mass-in-mass lattice structure, the periodic metacomposite has graded internal masses in each period. Referring to lumped-mass method and on the basis of Bloch theorem, the general formula for calculating the dispersion curve of the 1D periodic graded metacomposites is derived. Furthermore, the effects of the unit-cell's parameters including the mass and the spring constants are also investigated. Numerical results show that the number of the bandgaps is closely related to the number of the unit-cells in each period. The width and the location of the bandgaps are determined by the arrangement and the values of the mass and spring constants.