Theoretical investigation of the behavior of an acoustic metamaterial with extreme Youngʹs modulus

A mechanical model with local resonators is proposed as an acoustic metamaterial that exhibits an unusual frequency-dependent effective stiffness. If treated as an equivalent elastic solid, its effective Youngʹs modulus can become unbounded or vanishingly small at two respective frequencies. Moreover, in a certain frequency range, the effective Youngʹs modulus would become negative, resulting in a band gap that coincides with this frequency range. The wave attenuation behavior and mechanism are studied through numerical simulations on the acoustic metamaterial model. The capability of the metamaterial to selectively block or filter unwanted waves is demonstrated by a numerical simulation example.