## 4 Experiments  
Experiments were performed on a partially connected double beam in order to verify the proposed method in Section 2. Figure 6 shows the double layer beam, which was composed of two identical aluminum cantilever beams (350 mm \(\times\) 50 mm \(\times\) 1 mm) with one end clamped and the other end fixed with glue. The glue was evenly distributed along the longitudinal direction of the beam for 20 mm. As shown in the figure, the exciter was located on the clamped side and the force transducer was located between the exciter and the double beam system. The vibration induced by the exciter was measured with an accelerometer, which was located in same position as the accelerator (Acc. 1). In order to verify the proposed method, several experiments were conducted, as introduced in the theory section. Experiments were performed while increasing the voltage applied to the exciter twice. In these experiments, a linear relationship between the force and the applied voltage was assumed. The linear relationship was confirmed by attaching accelerometers to the area where the beams were glued. In the figure, the magnitude of the relative acceleration measured by Acc. 2 and Acc. 3 doubled in successive experiments. Thus, there was a linear relationship between the applied force and the voltage. The experiment was performed ten times from 5 mV to 2.56 V. The excitation frequency varied from 50 to 450 Hz based on the reliability of the exciter and the step sine used 2 Hz intervals. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**v-1**} & \multicolumn{2}{c}{**2\({}^{\text{nd}}\) Mode**} & \multicolumn{2}{c}{**4\({}^{\text{th}}\) Mode**} & \multicolumn{2}{c}{**6\({}^{\text{th}}\) Mode**} \\  & **Inverse** & **Newmark** & **Inverse** & **Newmark** & **Inverse** & **Newmark** \\  & **Matrix (\%)** & **Method (\%)** & **Matrix (\%)** & **Method (\%)** & **Matrix (\%)** & **Method (\%)** \\ \hline
0 & 13.199 & 10.574 & 31.887 & 15.272 & 100.000 & 100.000 \\
1 & 9.937 & 7.214 & 28.839 & 12.608 & 135.950 & 37.369 \\
2 & 8.675 & 5.913 & 28.704 & 12.490 & 67.009 & 2.768 \\
3 & 10.367 & 7.656 & 22.844 & 7.368 & 67.679 & 2.379 \\
4 & 18.818 & 16.363 & 22.321 & 6.911 & 68.544 & 1.875 \\
5 & 117.323 & 123.895 & 21.789 & 6.446 & 64.167 & 4.423 \\
6 & 217.785 & 227.395 & 20.967 & 5.727 & 61.796 & 5.804 \\
7 & 169.117 & 177.255 & 59.959 & 39.806 & 58.587 & 7.672 \\
8 & 63.680 & 68.630 & 295.122 & 245.344 & 54.384 & 10.119 \\
9 & 69.430 & 68.505 & 306.771 & 255.524 & 239.717 & 97.781 \\
10 & 132.867 & 133.861 & 292.655 & 243.187 & 385.652 & 182.743 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of the errors of the estimated \(\overline{R}\) compared to the obtained \(R\). Figure 7 shows the FRFs measured in the 10 experiments performed. The second mode in the figure shows that the peak values at the resonance frequency decreased as the applied force increased. That is, the mode shape at the contact region was predominantly governed by the slip phenomenon by out-of-mode shape. Other modes were independent to the magnitude of the external force. Typically, this tendency is confirmed by the peak value in the fifth mode. In order to estimate the variation of natural frequencies and damping ratios in response to a change in external force, the two parameters of the Iwan model were estimated. The proposed method was applied to the measurements from the first seven experiments. The natural frequencies and damping ratios of the remaining three experiments were predicted using the estimated two parameters. The modal parameters, natural frequency, and damping ratio, predicted using the estimated two parameters from the remaining three experiments, were compared with the estimated modal parameters from the real measurements of the same experiments. First, Equation (35) was applied to the second mode in the figure. The resultant \(y_{v}\) values showed a large deviation at a small force level and a nearly linear trend where the force was increased.