1. Microstructural design studies for locally dissipative acoustics 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 (MO) 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.
2. Dynamic load mitigation using negative effective mass structures
Structures created by incorporating resonating endo-structures within a load bearing exo-structure forbid dynamic disturbances within a specific frequency range from propagating into them without attenuations. Their dynamic behavior can be characterized using a negative effective mass (NM) density. The suitability of such negative effective mass structures (NMS) as infrastructural building-blocks implicitly less susceptible to both harmonic and broadband impact-type loadings is demonstrated. For harmonic loading, an apparent damping coefficient is derived to compare the degree of attenuation achieved in the wholly elastic NMS to an “equivalent” conventionally damped structure. Parametric studies were used to design and construct a low-frequency vibration isolator with tip-loaded cantilever beam resonators that evinced 98% payload isolation at resonance. Under impact loading, using a numerical optimization procedure, it was established that resonator frequencies towards the higher end of the incoming spectrum gave the most reduction in transmitted peak stress. Compact and efficient resonators were constructed using plate springs with chemically etched reentrant patterns and high density resonator mass material. Tests performed using an impact pendulum on a resonator stack attached to a transmission bar, substantiated a peak stress reduction of about 60% and filtering of the resonator frequencies in the transmitted spectrum. Further, drop tower tests performed on a NM infrastructural building-block to gauge its ability to mitigate shocks transmitted to a target structure relative to a mass-equivalent block of steel demonstrated a 25% reduction in peak transmitted acceleration.