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Recording of resonance spectrum in liquid. (a) Schematic of homemade measurement setup. The cantilevers are excited by a piezoelement beneath the cantilever chip body through a frequency generator. The cantilevers are rotated by 45° with respect to the liquid cell (dashed line). The read out of the cantilever response signal is performed by a laser deflection system. The frequency analyzer compares the signal from the cantilever with the excitation signal and records amplitude and phase spectra. (b) Complete amplitude and phase spectrum in water; the numbers indicate the mode of cantilever vibration. The amplitude peak of mode 1 is presented as inset. The signal transfer function is discussed in the supplementary material.
Comparison of experimental eigenfrequencies (red) with the frequencies predicted by different models (black). (a) Absolute frequencies. (b) Relative deviation of the models from the experimental values. Average deviations are 32% (Inviscid model), 4.4% (Elmer–Dreier), 30% (viscous), and 7.1% (extended viscous model). Note that the determination of the eigenfrequencies at modes 1 and 2 is difficult due to the high damping and the signal transfer function resulting in relative high experimental errors.
The measured quality factors and virtual mass are compared with model predictions. (a) Quality factors from the amplitude spectra [Fig. 1(b)] compared with the viscous and the extended viscous model. (b) Ratio between the virtual mass and the cantilever mass. Experimental values from the measured eigenfrequency compared with the best matching model from Fig. 2 (Elmer–Dreier model).
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