Tunable solid acoustic metamaterial with negative elastic modulus

We report in this letter on a tunable solid acoustic metamaterial with negative elastic modulus by means of piezoelectric composite. The theoretical formulae for one-dimensional layer-stacked metamaterial embedding a piezoelectric material by means of external shunted inductors are presented. The acoustic band structure of the composite is calculated by the transfer matrix method. Results show that a band gap can be opened and tuned by the resonant behavior of the LC circuit. It is found further by the formulae that piezoelectric material with large piezoelectric constant and small elastic modulus will be beneficial for opening a wide band gap. The effective elastic constant of the system is also calculated by the unit-cell-boundary-averaging method. Result shows that the system behaves as an effective medium with a negative elastic modulus. This property is quite different from the typical solid metamaterial achieved by dispersing heavy inclusions coated with a soft layer into a matrix for which only the negative mass density can be obtained.