Precise velocity measurements for driven intrinsic localized modes in the acoustic spectrum of small cantilever arrays

Abstract

The speed of a traveling intrinsic localized mode (ILM) in the acoustic spectrum of a micromechanical cantilever array is experimentally measured at high resolution as a function of the driving frequency. A repeating speed pattern is observed for chaotic and regular traveling ILMs between adjacent extended wave normal mode frequencies. The speed of a regular traveling ILM is almost the same as the plane wave dispersion group velocity at that frequency. Since ILM amplification only occurs during reflections at the ends of the array the phase matching condition for long time stability is greatly relaxed. A double humped distribution of speeds, found for chaotic ILMs, is shifted from the regular ILM nearly monochromatic speed value due to the modulational instability. Numerical simulations reproduce many of the experimental observations, demonstrating that intrinsic dynamical properties of the small array are being measured.