# Experimental Study of See-Saw Mode Nano-Vibration on Orifice-Type Restrictors
## 2 Materials and Methods
### Simulation on One-Orifice-Type Restrictor Based on FEM FSI  
An FEM FSI was built as shown in Figure 2. The restrictor and gas film metrics are as shown in Figure 1. The computer configuration was as follows: CPU Intel X5650 2.6 GHz, 24-GB RAM, Matrox G200 eV (Winbond) integrated graphics and a 2-terabyte hard disk. The restrictor is set into 20 layers, and the gas is five layers. The gas in the FEM model was set to a dynamic grid with a Yeoh smoothing type. Then, 19,725 grids were obtained with an average mesh quality >0.89. Finally, the structure was set to forge aluminum 6061 with a density, \(\rho_{s}=2.75\) g/cm\({}^{3}\), Young's modulus, \(E=205\) MPa and Poisson ratio, \(\mu_{s}=0.33\). The gas parameters were set to \"air\" with a coefficient of kinetic viscosity, \(\mu_{g}=\) Pa/s, air density, \(\mu_{g}=1.225\) kg/m\({}^{3}\) and gauge-pressure-at-outlet, 0 Pa. With the FEM FSI model, each grid at the interface was a fluid-structure interface set with equilibria of stress (\(\tau\)), displacement (\(d\)), heat flux (\(q\)) and temperature (\(T\)), as shown in Equation (2) [16]:  
Figure 1: Orifice-type and its equivalent model: (**a**) axial section of the restrictor; (**b**) equivalent spring model; and (**c**) one-orifice model. \[\left\{ \begin{array}{c}\tau_{f}\cdot n_{f}=\tau_{s}\cdot n_{s}\\ d_{f}=d_{s}\\ q_{f}=q_{s}\\ T_{f}=T_{s}\end{array} \right. \tag{2}\]  
where the subscripts, \(f\) and \(s\), are fluid and solid, respectively. In CFD, the steady-state calculation result from the Reynolds average Navier-Stokes (RANS) of the basin was used as the initial value of the transient simulation. Furthermore, the fluid in FSI model was calculated in large eddy simulation (LES). The solution length was set to 0.0001 s, and the total time as 0.005 s. The convergence of the results is default, 0.0001. The transient characteristics and the average amplitude characteristics of the normal vibration of the restrictor were obtained. Figure 3 shows the results of the transient normal amplitude distribution, \(A\), under different inlet air velocities, \(v_{a}\). Figure 3: Transient normal vibration \(A\) results under different inlet air velocities \(v_{a}\) at different instantaneous time \(T\) from FEM FSI model: (**a**) \(v_{a}\) = 0.002 m/s; (**b**) \(v_{a}\) = 0.004 m/s; (**c**) \(v_{a}\) = 0.006 m/s; and (**d**) \(v_{a}\) = 0.008 m/s. Figure 2: FEM FSI meshing: (**a**) refined meshing at inlet; (**b**) meshing at the upper surface; and (**c**) sweep meshing from top to bottom. Figure 4 shows the time-averaged normal amplitude, \(A_{a}\), at different inlet gas flow velocities, \(v_{a}\). Here, we did not set the inlet air pressure, owing to the simplified FEM FSI. However, it is certain that the air velocity, \(v_{a}\), is determined by the air-supply and the restrictor parameters if the load is stable or none. When increasing the inlet air velocity, \(v_{a}\), in the FEM FSI model, the simulation solution failed, probably because of the computer configuration, according to a COMSOL technicians' consultation. Fortunately, we made some compelling findings. From the simulation results, we present the following findings. 1. The restrictor presents normal linear vibration and rotation, which is consistent with the equation of motion given by Equation (1). The change in displacement shown in Figure 3 supports this well. 2. The rotational axis passes through the center of gravity in the \(xy\) plane (Figure 3), but it is not restricted to the \(x\) or \(y\) axes. The average normal amplitude is equal along the circumference, as shown in Figure 4, which means the rotation axis can be random. 3.