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

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