Optimization of uncertain acoustic metamaterial with Helmholtz resonators based on interval model

Abstract

Uncertainties existing in the acoustic metamaterial may strongly affect its unusual properties. Aiming at this actuality, the interval model is introduced to treat with uncertainties existing in the acoustic metamaterial with Helmholtz resonators. Frequency intervals in which the sound intensity transmission coefficients are certainly less than the required value and the effective bulk moduli are certainly negative are defined as conservative approximations. Frequency intervals in which the sound intensity transmission coefficients may be less than the required value and the effective bulk moduli may be negative are defined as unsafe approximations. The proportion of the conservative approximation and the unsafe approximation is defined as an approximate precision. Based on the quantification of uncertainties of the sound intensity transmission coefficients and the negative effective bulk moduli, an optimization model for the interval acoustic metamaterial with Helmholtz resonators is constructed. Numerical results showed that even suffering from effects of interval parameters, unusual properties of the optimized acoustic metamaterial (such as the bandgap of the sound transmission and the negative effective bulk modulus) could be improved.