Definition of the various lengths and widths in the spring constant and resonance frequency models.
Model behavior for the modified spring constant of a cantilever of the general form expressed in Fig. 1 as derived in Eq. (2).
Model behavior of the resonance frequency of the modified cantilevers from Eq. (5).
The total mass of a modified cantilever, .
Model behavior of the effective mass of a modified cantilever which is mass loaded at from Eq. (11).
Distributed mass sensitivity over the hole parameter space as determined by Eq. (14). Although the range of the function is , the vertical scale is presented from 0 to 2 so as to display clearly the behavior of the function across the entire parameter space.
Point mass sensitivity, , over the hole parameter space determined from Eq. (15).
Mass sensitivity regions of increased and decreased mass sensitivity with respect to the URC. The open symbols represent data points generated from the analytical model, whereas the solid lines represent empirical fits to Eq. (16) with fitting parameters presented in Table II. Cantilevers above the curves within the , plane will exhibit increased mass sensitivity with respect to the URC, whereas cantilevers below the curves will exhibit decreased mass sensitivity. Between the curves, the cantilevers will exhibit increased distributed mass sensitivity, but decreased point mass sensitivity.
Representative lever from a cantilever array, (a) before and (c) after modification with the FIB, as well as the thermal noise spectra for the same lever (b) before and (d) after modification. The cantilever width in both images is . The box appearing in (a) is the template for the hole pictured in (c).
Mesh for FEA of a representative MRC (hole fractions and ). The properties of interest (, , ) are determined from the (a) the URC, and the modified properties (, , ) from (b) the MRC. The base of each lever (fixed end) is the left of the image, and the free end is the right of the image.
Comparison of the analytical models (—) with the FEA results (◻),and the experimental results (◯). Plots (a), (c), and (e), represent variation in the width of the hole (variable ) while keeping the length constant . Plots (b), (d), and (f) represent variation in the length of the hole (variable ) while keeping the width constant .
Graphic representation of the limiting cases of the modified cantilever geometry and the expected behavior of the levers in the limiting cases.
Fitting parameters for Eq. (16) from the analytical model.
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