## 5 Results
### Simulation Results
#### 5.2.6 Influence of the Pipette Radius  
More than the pipette wall thickness, specimen thickness and specimen radius, the radius of the pipette can affect the results. In [PERSON] et al. [33], the static measurement setup assumed that a change in the pipette radius causes a change in the displacement amplitude with an equal ratio. In other words, increasing or decreasing the pipette radius will cause an increase or decrease in the displacement amplitude with an equal factor. While the measured displacement from our dynamic experimental setup is revealed to have high dependency on the radius of the pipette with respect to the excitation frequency, the frequency-dependent relation violates the [PERSON] et al. [33] assumption after a certain radius size and especially in frequencies higher 100 Hz. This behaviour is seen also in the simulation results as follows: Figure 16 shows the \(z\)-component of the simulated displacement amplitude in the center of the pipette versus the frequency range by six different pipette radii. The displacement is almost constant over the frequency range using a very small radius, 0.25 mm, while, in both boundary conditions, the displacement amplitude is a function of the excitation frequency for radii larger than 0.25 mm. The displacement grows with increasing frequency in radii lower than 1.25 mm, but this trend will inverse if the pipette radius exceeds 1.25 mm. For the higher radii 3.25 mm, 4.25 mm and 5.25 mm, the displacement falls with moving forward in the frequency steps. Consequently, the displacement has a nonlinear relation with the pipette radius after a certain radius, so the radius could not exceed a certain limit in a dynamic measurement. It can be supposed from a static measurement that, if the pipette encloses the surface with a larger radius, the generated displacement should have a higher amplitude because of the larger space for vibration, while, with harmonic excitation, the larger space made the surface able to resonate. This can be concluded from Figure 16 where the displacement amplitude (in the centre of the pipette) falls more in the higher radii. In both boundary conditions, a high radius causes resonance on the surface after 100 Hz excitation frequency. Therefore, the displacement amplitude on the centre of the pipette is decreased significantly. Similar to the [PERSON] et al. [33] static measurement, the increasing ratios of the displacement amplitude and the radius are equal in 50 Hz excitation frequency. To explain better, the resonance behaviour of the model as a function of the pipette radius, the surface plot of the displacement amplitude generated by 500 Hz excitation frequency for two different radii 1.25 mm and 5.25 mm are illustrated in Figures 17 and 18. The displacement \(z\)-component of the connected pipette boundary condition is shown in Figure 17 and, of the pipette with gap boundary condition, shown in Figure 18. All the simulation conditions are exactly the same as Sections 5.2.1 and 5.2.2 except a phase (\(\pi\)) assigned to the fluctuating force \(p_{m}\) to make the behaviour of the model in the plots more understandable. The scale factor of the plots is 1000. As are shown in Figure 17a and Figure 18a, the high radius of the pipette made the surface resonant; as a result, the maximum displacement amplitude falls and moves from the centre of the pipette. Figure 17b shows that the maximum displacement amplitude of the 1.25 mm surface radius 2.75 mm in the centre of the pipette. While, because of the resonance induced due to the larger radius 5.25 mm, the maximum displacement falls from 2.75 mm to 1.24 mm and moves from the centre, as is depicted in Figure 17a. Moreover, the displacement amplitude in the centre of the pipette declines from 2.75 mm in radius 1.25 mm to almost 0.5 mm in the radius 5.25 mm. The same behavior in the pipette with gap boundary condition is visible from Figure 18. However, the resonance effect is weaker because the model surface is not restricted by the pipette wall in this boundary condition.