Dynamic load mitigation using negative effective mass structures

• Dynamic load mitigation for structural systems that display effective “negative mass”.
• Derivation of apparent damping corresponding to the attenuation produced by “negative mass”.
• Design of “negative effective mass” structures.
• Performance evaluation by simulations and experiments.

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. It was found that the higher the stiffness of the host structure, the narrower the isolation bandwidth is in the vicinity of the resonance frequency. Under impact loading, using a numerical optimization procedure, it was established that resonator frequencies toward the higher end of the incoming spectrum gave better reduction in transmitted peak stress. Compact and efficient resonators were constructed using plate springs with chemically etched reentrant patterns and machined titanium resonator masses. 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.