Microstructural design studies for locally dissipative acoustic metamaterials

Stress wave attenuation performance of locally dissipative acoustic metamaterials with various damped oscillator microstructures is studied using mechanical lattice models. The presence of damping is represented by a complex effective mass. Analytical solutions and numerical verifications of transmissibility are obtained for Kelvin-Voigt-type (KVO), Maxwell-type, and Zener-type (ZO) oscillators with viscous damping. Although peak attenuation at resonance is diminished, dissipative microstructures can provide broad spectrum attenuation without increasing mass ratio, obviating the bandgap width limitation of locally resonant microstructures. KVO gives the best broad spectrum performance akin to a low-pass filter for excitation frequencies above a cut-off value for a prescribed transmissibility criterion. For ZO, by tailoring the damping and stiffness, the frequency range of appreciable attenuation can at least span the bandgap widths of two limiting locally resonant cases. Static and frequency-dependent measures of optimal damping that maximize the attenuation characteristics are proposed. A transitional value for the excitation frequency is identified within the locally resonant bandgap, above which there always exists an optimal amount of damping that renders the attenuation for the dissipative metamaterial greater than that for the locally resonant case. Further microstructures with hysteretic damping depict a frequency-independent scaling in the effective mass and attenuation factor, but the bandgap width remains nearly the same as that for the corresponding viscously damped microstructures. This study demonstrates that dissipative microstructures, which are to some extent unavoidable in practical designs, when tuned, provide a means to substantially enhance the attenuation bandwidth of locally resonant acoustic metamaterials while also enabling the removal of the energy sequestered by the oscillators from the system. (C) 2014 AIP Publishing LLC.