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This study proposes the use of a linear and geometrically nonlinear inerter-based resonator in locally resonant acoustic metamaterials (LRAMs) and evaluates the performance on low-frequency wave attenuation. The LRAM is modeled as a 1D chain system composed of mass-in-mass unit cells connected by springs, and the geometrical nonlinearity is achieved by two lateral inerters linking the resonator and lumped mass symmetrically with respect to the horizontal springs. For the nonlinear inerter-based LRAM, the dispersion relation is analytically derived by a complex Fourier transform and the harmonic balance method. Compared with the linear inerter-based LRAM, the proposed nonlinear inerter-based structure has the property of a low-frequency bandgap with sufficient width for longitudinal wave propagation without being sensitive to changes in the inertance ratio. The nonlinearity can extend the original material parameter restrictions, leading to a lower-frequency bandgap. The results of dispersion properties are validated by wave transmittance and vibration power flow diagrams obtained by using the method of effective mass. It is shown that an adequate number of unit cells can achieve better wave attenuation performance.

Enhanced suppression of low-frequency vibration transmission in metamaterials with linear and nonlinear inerters