## 3 Damage Comparison with a Uniaxial Vibration Test
### Discussion  
The calculated fatigue damages listed in Table 2 show that the repeatability of the test results was effectively guaranteed for the same test mode, except for the sine-on-random case. In the case of the random test, the deviation of the three physical damages was partially visible because the amplitude of the strain was low enough to be damaged by unexpected noises. The damage variation was larger in the sine-on-random test case compared to the other test modes: the harmonic and random. This was a result of the multi-spectral pattern source, making it difficult to control the phase of the response data compared to a conventional single-spectral pattern source. Thus, the maximum spectral peak of the response data could have changed slightly during the test, which explains the significant variation in the fatigue damage. The severity of the fatigue damage was more visible in the pseudo-damage than the physical damage. In Table 3, the damage ratios for the two spectral cases, random and harmonic, are 0.02% and 43.3%, respectively, for the pseudo-damage, whereas these damage ratios are less than 0.01% and 79.3%, respectively, for the physical damage. Therefore, no single spectral pattern test (random or harmonic only) can supersede the severity of a sine-on-random test. Even a series of tests under a \begin{table}
\begin{tabular}{c c c c c} \hline
**Mode** & **\#** & **Pseudo Damage** & **\#** & **Physical Damage** \\ \hline \multirow{4}{*}{Random} & 1 & \(1.10\times 10^{-4}\) & 1 & \(1.70\times 10^{-10}\) \\  & 2 & \(1.55\times 10^{-4}\) & 2 & \(9.95\times 10^{-10}\) \\  & 3 & \(1.08\times 10^{-4}\) & 3 & \(3.23\times 10^{-10}\) \\  & Avg. & \(1.24\times 10^{-4}\) & Avg. & \(4.96\times 10^{-10}\) \\ \hline \multirow{4}{*}{Harmonic} & 1 & \(2.92\times 10^{-1}\) & 1 & \(5.97\times 10^{-5}\) \\  & 2 & \(3.00\times 10^{-1}\) & 2 & \(6.01\times 10^{-5}\) \\ \cline{1-1}  & 3 & \(2.93\times 10^{-1}\) & 3 & \(6.28\times 10^{-5}\) \\ \cline{1-1}  & Avg. & \(2.95\times 10^{-1}\) & Avg. & \(6.09\times 10^{-5}\) \\ \hline \multirow{4}{*}{Sine-on-Random} & 1 & \(7.48\times 10^{-1}\) & 1 & \(1.02\times 10^{-4}\) \\  & 2 & \(7.47\times 10^{-1}\) & 2 & \(7.03\times 10^{-5}\) \\ \cline{1-1}  & 3 & \(5.52\times 10^{-1}\) & 3 & \(5.76\times 10^{-5}\) \\ \cline{1-1}  & Avg. & \(6.82\times 10^{-1}\) & Avg. & \(7.67\times 10^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Accumulated spectral fatigue damage over different spectral loading patterns and damages. Figure 5: Acceleration responses of notched simple specimen at #2: sine-on-random excitation; \(\epsilon\) harmonic excitation; and \(\epsilon\) random excitation. \begin{table}
\begin{tabular}{c c c} \hline
**Mode** & **Pseudo Damage** & **Physical Damage** \\ \hline Random & 0.02 (\%) & Less than 0.01 (\%) \\ Harmonic & 43.3 (\%) & 79.3 (\%) \\ \hline \end{tabular}
\end{table} 
Table 3: Damage ratios between single spectra and sine-on-random. single spectrum input, random after harmonic or in reverse order, is not sufficient to supplant the sine-on-random test in regard to fatigue damage. In addition, the fatigue damage from a noise source is considerably less than that from a harmonic one because even the single peak response from harmonic excitation leads to critical damage to the test specimen compared to the numerous spectral responses from a noise source. The pseudo-damage referenced in ISO 16750-3 is only a criterion for grading the severity of a test mode. In contrast, the accumulated damage derived from Equation (7) is a real damage value related to crack initiation, and is a good match for the failure mode of a vibration test. Thus, the physical fatigue damage results were used to compare the test severities over different spectral loading patterns, where the physical damage ratio from random excitation was less than 0.01% and the harmonic excitation was 79.3%, as listed in Table 3. The random excitation alone had little impact on the fatigue damage of the notched simple specimen.