Mode-shape-based mass detection scheme using mechanically diverse, indirectly coupled microresonator arrays

Abstract

We explore vibration localization in arrays of microresonators used for ultrasensitive mass detection and describe an algorithm for identifying the location and amount of added mass using measurements of a vibration mode of the system. For a set of sensing elements coupled through a common shuttle mass, the inter-element coupling is shown to be proportional to the ratio of the element masses to the shuttle mass and to vary with the frequency mistuning between any two sensing elements. When any two elements have sufficiently similar frequencies, mass adsorption on one element can result in measurable changes to multiple modes of the system. We describe the effects on system frequencies and mode shapes due to added mass, in terms of mass ratio and frequency spacing. In cases in which modes are not fully localized, frequency-shift-based mass detection methods may give ambiguous results. The mode-shape-based detection algorithm presented uses a single measured mode shape and corresponding natural frequency to identify the location and amount of added mass. Mass detection in the presence of measurement noise is numerically simulated using a ten element sensor array. The accuracy of the detection scheme is shown to depend on the amplitude with which each element vibrates in the chosen mode.